1. UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Moharram Aghapournahr

Volume 1, Issue 1 , Summer and Autumn 2013, , Pages 1-9

Abstract

  Let $R$ be a commutative Noetherian ring with non-zero identity and $a$ an ideal of $R$. Let $M$ be a finite $R$--moduleof finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $H^{i}_{a}(M,N)$ in certain Serre ...  Read More Let $R$ be a commutative Noetherian ring with non-zero identity and $a$ an ideal of $R$. Let $M$ be a finite $R$--moduleof finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $H^{i}_{a}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $\mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $H^{i}_{a}(M,N)$ belongs to $\mathcal S$ for all $i> n$. Then, for any ideal $b\supseteq a$, it is also shown that the module $H^{n}_{a}(M,N)/{b}H^{n}_{a}(M,N)$ belongs to $\mathcal S$.

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2. ON COMULTIPLICATION AND R-MULTIPLICATION MODULES

A. Nikseresht; H. Sharif

Volume 2, Issue 1 , Summer and Autumn 2014, , Pages 1-19

Abstract

  We state several conditions under which comultiplication and weak comultiplication modules are cyclic and study strong comultiplication modules and comultiplication rings. In particular, we will show that every faithful weak comultiplication module having a maximal submodule over a reduced ring with ...  Read More We state several conditions under which comultiplication and weak comultiplication modules are cyclic and study strong comultiplication modules and comultiplication rings. In particular, we will show that every faithful weak comultiplication module having a maximal submodule over a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplication R-module, then R is semilocal and M is finitely cogenerated.Furthermore, we define an R-module M to be p-comultiplication, if every nontrivial submodule of M is the annihilator of some prime ideal of R containing the annihilator of M and give a characterization of all cyclic p-comultiplication modules. Moreover, we prove that every pcomultiplication module which is not cyclic, has no maximal submodule and its annihilator is not prime. Also we give an example of a module over a Dedekind domain which is not weak comultiplication, but all of whose localizations at prime ideals are comultiplication and hence serves as a counterexample to [10, Proposition 2.3] and [11, Proposition 2.4].

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3. THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES

M. Aghapournahr; Kh. Ahmadi-amoli; M. Sadeghi

Volume 3, Issue 1 , Summer and Autumn 2015, , Pages 1-10

Abstract

  ‎We introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay ...  Read More ‎We introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modules‎. ‎These kind of modules are different from Cohen--Macaulay modules‎, as an example shows‎. ‎Also an artinian result for such modules is given‎.

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4. ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

A. Pourmirzaei; M. Hassanzadeh; B. Mashayekhy

Volume 4, Issue 1 , Summer and Autumn 2016, , Pages 1-13

Abstract

  Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties ...  Read More Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N) under some extraassumptions.

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5. MOST RESULTS ON A-IDEALS IN MV -MODULES

S. Saidi Goraghani; R. A. Borzooei

Volume 5, Issue 1 , Summer and Autumn 2017, , Pages 1-13

Abstract

  In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not ...  Read More In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $K\subseteq \bigcup _{i=1}^{n}K_{i}$ implies $K\subseteq K_{j}$, where $K,K_{1},\cdots ,K_{n}$ are A-ideals of A-module M and $1\leq j\leq n$.

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6. MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM

M. Farhadi Sangdehi

Volume 6, Issue 1 , Summer and Autumn 2018, , Pages 1-12

Abstract

  We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms ...  Read More We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

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7. BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

E. Hashemi; Kh. Khalilnezhad; M. Ghadiri

Volume 7, Issue 1 , Summer and Autumn 2019, , Pages 1-24

Abstract

  A ring $R$ with an automorphism $\sigma$ and a $\sigma$-derivation $\delta$ is called $\delta$-quasi-Baer (resp., $\sigma$-invariant quasi-Baer) if the right annihilator of every $\delta$-ideal (resp., $\sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we ...  Read More A ring $R$ with an automorphism $\sigma$ and a $\sigma$-derivation $\delta$ is called $\delta$-quasi-Baer (resp., $\sigma$-invariant quasi-Baer) if the right annihilator of every $\delta$-ideal (resp., $\sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=\sigma(R)\left\langle x_{1},\ldots,x_{n}\right\rangle $ be a skew PBW extension of derivation type of a ring $R$. (i) It is shown that $ R$ is $\Delta$-quasi-Baer if and only if $ A$ is quasi-Baer.(ii) $ R$ is $\Delta$-Baer if and only if $ A$ is Baer, when $R$ has IFP. Also, let $A=\sigma (R)\left\langle x_1, \ldots , x_n\right\rangle$ be a quasi-commutative skew PBW extension of a ring $R$. (iii) If $R$ is a $\Sigma$-quasi-Baer ring, then $A $ is a quasi-Baer ring. (iv) If $A $ is a quasi-Baer ring, then $R$ is a $\Sigma$-invariant quasi-Baer ring. (v) If $R$ is a $\Sigma$-Baer ring, then $A $ is a Baer ring, when $R$ has IFP. (vi) If $A $ is a Baer ring, then $R$ is a $\Sigma$-invariant Baer ring. Finally, we show that if $A = \sigma (R)\left\langle x_1, \ldots , x_n\right\rangle $ is a bijective skew PBW extension of a quasi-Baer ring $R$, then $A$ is a quasi-Baer ring.

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8. MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Y. Tolooei

Volume 8, Issue 1 , Summer and Autumn 2020, , Pages 1-5

Abstract

  Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules ...  Read More Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a characterization of finitely generated multiplication modules.

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9. SOME RESULTS ON STRONGLY PRIME SUBMODULES

A.R. Naghipour

Volume 1, Issue 2 , Winter and Spring 2014, , Pages 79-89

Abstract

  Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. In this paper, we study more properties of strongly prime submodules. It is shown that a ...  Read More Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every strongly prime submodule of $M$ is maximal. We also study the strongly dimension of a module which is defined to be the length of a longest chain of strongly prime submodules.

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10. ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES

Modjtaba Ghorbani; Mina Rajabi-Parsa

Volume 6, Issue 2 , Winter and Spring 2019, , Pages 81-89

Abstract

  A permutation with no fixed points is called a derangement. The subset $\mathcal{D}$ of a permutation group is derangement if all elements of $\mathcal{D}$ are derangement. Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $\mathcal{D}$ as connecting ...  Read More A permutation with no fixed points is called a derangement. The subset $\mathcal{D}$ of a permutation group is derangement if all elements of $\mathcal{D}$ are derangement. Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $\mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

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11. ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES

M. Jafarpour; F. Alizadeh

Volume 2, Issue 2 , Winter and Spring 2015, , Pages 83-96

Abstract

  In this paper using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups $Z_{2n}$ and $Z_{n}times Z_{2}$ produce a strongly duplex and ...  Read More In this paper using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups $Z_{2n}$ and $Z_{n}times Z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

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12. FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES

M. Rezaei; Z. Foruzanfar

Volume 4, Issue 2 , Winter and Spring 2017, , Pages 85-95

Abstract

  ‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define kG(A)‎, ‎the number of conjugacy classes of G that intersect A non-trivially‎. ‎In this paper‎, ‎we verify the structure of all finite groups G which satisfy the property ...  Read More ‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define kG(A)‎, ‎the number of conjugacy classes of G that intersect A non-trivially‎. ‎In this paper‎, ‎we verify the structure of all finite groups G which satisfy the property kG(G-Z(G))=5, and classify them‎.

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13. A COVERING PROPERTY IN PRINCIPAL BUNDLES

A. Pakdaman; M. Attary

Volume 5, Issue 2 , Winter and Spring 2018, , Pages 91-98

Abstract

  Let $p:X\lo B$ be a locally trivial principal G-bundle and $\wt{p}:\wt{X}\lo B$ be a locally trivial principal $\wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $\wt{G}$ is a covering group of $G$ if and only if $\wt{X}$ is a covering ...  Read More Let $p:X\lo B$ be a locally trivial principal G-bundle and $\wt{p}:\wt{X}\lo B$ be a locally trivial principal $\wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $\wt{G}$ is a covering group of $G$ if and only if $\wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal covering space has no connected locally trivial principal $\pi(X,x_0)$-bundle, for every $x_0\in X$.

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14. AMENABILITY OF VECTOR VALUED GROUP ALGEBRAS

Ali Ghaffari; Seyedeh Samaneh Javadi Syahkale

Volume 3, Issue 2 , Winter and Spring 2016, , Pages 97-107

Abstract

  The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, ...  Read More The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

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15. SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP

S. Visweswaran; P. Vadhel

Volume 7, Issue 2 , Winter and Spring 2020, , Pages 105-130

Abstract

  Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is ...  Read More Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the graph-theoretic properties of the complement of the intersection graph of subgroups of G.

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16. CLASSICAL 2-ABSORBING SECONDARY SUBMODULES

F. Farshadifar

Volume 8, Issue 1 , Summer and Autumn 2020, , Pages 7-15

Abstract

  ‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We ...  Read More ‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎\emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a‎, ‎b \in R$‎, ‎$K$ is a submodule of $M$ and $abN\subseteq K$‎, ‎then $aN \subseteq K$ or $bN \subseteq K$ or $ab \in \sqrt{Ann_R(N)}$‎. ‎This can be regarded as a dual notion of the 2-absorbing primary submodule‎.

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17. f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS

L. Kamali Ardakani; Bijan Davvaz

Volume 1, Issue 1 , Summer and Autumn 2013, , Pages 11-31

Abstract

  Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations ...  Read More Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.

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18. AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

S. Karimzadeh; R. Nekooei

Volume 3, Issue 1 , Summer and Autumn 2015, , Pages 11-22

Abstract

  In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going ...  Read More In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

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19. SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL

E. Ghasemian; Gh. H. Fath-Tabar

Volume 6, Issue 1 , Summer and Autumn 2018, , Pages 13-28

Abstract

  Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and ...  Read More Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

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20. SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

M. Ebrahimpour

Volume 4, Issue 1 , Summer and Autumn 2016, , Pages 15-27

Abstract

  Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed ...  Read More Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-known results about multiplicativelyclosed subsets of R are not valid for these generalized subsets ofM.

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21. AN INDUCTIVE FUZZY DIMENSION

M. Abry; Jafar Zanjani

Volume 5, Issue 1 , Summer and Autumn 2017, , Pages 15-25

Abstract

  Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen ...  Read More Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are established.

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22. DIFFERENTIAL MULTIPLICATIVE HYPERRINGS

L. Kamali Ardekani; B. Davvaz

Volume 2, Issue 1 , Summer and Autumn 2014, , Pages 21-35

Abstract

  There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative ...  Read More There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplicative hyperring, derivation, differential hyperring.

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23. COTORSION DIMENSIONS OVER GROUP RINGS

A. Hajizamani

Volume 7, Issue 1 , Summer and Autumn 2019, , Pages 25-32

Abstract

  Let $\Gamma$ be a group, $\Gamma'$ a subgroup of $\Gamma$ with finite index and $M$ be a $\Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $\Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $Z\Gamma$ and $Z\Gamma'$ are equal.  Read More Let $\Gamma$ be a group, $\Gamma'$ a subgroup of $\Gamma$ with finite index and $M$ be a $\Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $\Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $Z\Gamma$ and $Z\Gamma'$ are equal.

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24. A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS

M. Nasernejad

Volume 1, Issue 2 , Winter and Spring 2014, , Pages 91-100

Abstract

  In this paper, by using elementary tools of commutative algebra, we prove the persistence property for two especial classes of rings. In fact, this paper has two main sections. In the first main section, we let $R$ be a Dedekind ring and $I$ be a proper ideal of $R$. We prove that if $I_1,\ldots,I_n$ ...  Read More In this paper, by using elementary tools of commutative algebra, we prove the persistence property for two especial classes of rings. In fact, this paper has two main sections. In the first main section, we let $R$ be a Dedekind ring and $I$ be a proper ideal of $R$. We prove that if $I_1,\ldots,I_n$ are non-zero proper ideals of $R$, then ${Ass}^{\infty}(I_1^{k_1}\ldots I_n^{k_n})={Ass}^{\infty}(I_1^{k_1})\cup\cdots\cup {Ass}^{\infty}(I_n^{k_n})$ for all $k_1,\ldots,k_n \geq 1$, where for an ideal $J$ of $R$, ${Ass}^{\infty}(J)$ is the stable set of associated primes of $J$. Moreover, we prove that every non-zero ideal in a Dedekind ring is Ratliff-Rush closed, normally torsion-free and also has a strongly superficial element. Especially, we show that if $\mathcal{R}=\mathcal{R}(R, I)$ is the Rees ring of $R$ with respect to $I$, as a subring of $R[t,u]$ with $u=t^{-1}$, then $u\mathcal{R}$ has no irrelevant prime divisor. \par In the second main section, we prove that every non-zero finitely generated ideal in a Pr\"{u}fer domain has the persistence property with respect to weakly associated prime ideals.

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25. On $\alpha $-semi-Short Modules

Maryam Davoudian

Volume 6, Issue 2 , Winter and Spring 2019, , Pages 91-99

Abstract

  We introduce and study the concept of $\alpha $-semi short modules. Using this concept we extend some of the basic results of $\alpha $-short modules to $\alpha $-semi short modules. We observe that if $M$ is an $\alpha $-semi short module then the dual perfect dimension of $M$ is $\alpha $ ...  Read More We introduce and study the concept of $\alpha $-semi short modules. Using this concept we extend some of the basic results of $\alpha $-short modules to $\alpha $-semi short modules. We observe that if $M$ is an $\alpha $-semi short module then the dual perfect dimension of $M$ is $\alpha $ or $\alpha +1$. %In particular, if a semiprime ring $R$ is $\alpha $-semi short as an $R$-module, then its Noetherian dimension either is $\alpha$ or $\alpha +1$.

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