THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES
Moharram
Aghapournahr
Arak Aniversity
author
Khadijeh
Ahmadi-amoli
Payame Noor University, Tehran
author
Miryousef
Sadeghi
Payame Noor University, Tehran
author
text
article
2015
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
1
10
http://jas.shahroodut.ac.ir/article_482_3406cd1fa845d38b77f2556344be6005.pdf
dx.doi.org/10.22044/jas.2015.482
AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS
Somayeh
Karimzadeh
Vali-e-Asr university of Rafsanjan
author
Reza
Nekooei
Shahid Bahonar University of Kerman
author
text
article
2015
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
11
22
http://jas.shahroodut.ac.ir/article_483_975f783e6699718e23896ed95ef10f18.pdf
dx.doi.org/10.22044/jas.2015.483
GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
Alireza
Naghipour
Shahrekord University,
author
text
article
2015
eng
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
23
30
http://jas.shahroodut.ac.ir/article_484_b8aa3a43cefa546233e3447390d3917d.pdf
dx.doi.org/10.22044/jas.2015.484
GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE
M. A.
Mehrjoofard
Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
author
H. R.
Afshin
department of mathematics,
Vali-e-Asr University of Rafsanjan, Iran
author
S.
Bagheri
department of mathematics, Vali-e-Asr University of Rafsanjan
author
text
article
2015
eng
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generalized numerical ranges and quantum error correction, J. Operator Theory, 66: 2, 335-351.] are extended.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
31
38
http://jas.shahroodut.ac.ir/article_486_30a2c8fdb2eec77f2ced44e835d901de.pdf
dx.doi.org/10.22044/jas.2015.486
ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS
M.
Baziar
Yasouj University
author
text
article
2015
eng
In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $Bbb{A}_*(M)=emptyset$if and only if $M$ is a uniform module and ann$(M)$ is a primeideal of $R$.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
39
47
http://jas.shahroodut.ac.ir/article_487_8c19ee23c3f1660ea1bf09bce9b1e051.pdf
dx.doi.org/10.22044/jas.2015.487
HvMV-ALGEBRAS II
mahmood
bakhshi
teacher.bojnoord university.iran
author
text
article
2015
eng
In this paper, we continue our study on HvMV-algebras. The quotient structure of an HvMV-algebra by a suitable types of congruences is studied and some properties and related results are given. Some homomorphism theorems are given, as well. Also, the fundamental HvMV-algebra and the direct product of a family of HvMV-algebras are investigated and some related results are obtained.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
49
64
http://jas.shahroodut.ac.ir/article_488_e0ce643e38d53b19a931c7ee7e0298a6.pdf
dx.doi.org/10.22044/jas.2015.488
FUZZY NEXUS OVER AN ORDINAL
T.
Haghdadi
Birjand University of Technology
author
A. A.
Estaji
Faculty of Mathematics and Computer Sciences
, Hakim Sabzevari University
author
J.
Farokhi Ostad
Faculty of Basic Sciences, Birjand University of technology
author
text
article
2015
eng
In this paper, we define fuzzy subnexuses over a nexus $N$. Define and study the notions of the prime fuzzy subnexuses and the fractionsinduced by them. Finally, we show that if S is a meetclosed subset of the set Fsub(N), of fuzzy subnexuses of a nexus N, andh= ⋀S ϵ S, then the fractions S^-1 N and h^-1 N are isomorphic as meet-semilattices.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
65
82
http://jas.shahroodut.ac.ir/article_489_a9a4ba1f624488e61c5e37175e928284.pdf
dx.doi.org/10.22044/jas.2015.489
COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
M.
Jalali-Rad
University of Kashan
author
A. R.
Ashrafi
University of Kashan
author
text
article
2015
eng
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of order $4p$ or $p^3$, where $p$ and $q$ are primes.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
3
v.
1
no.
2015
88
95
http://jas.shahroodut.ac.ir/article_490_ad72cc6d7ccfdda1a417ad5e72b51945.pdf
dx.doi.org/10.22044/jas.2015.490