THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES
M.
Aghapournahr
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-
8349, Iran.
author
Kh.
Ahmadi-amoli
Department of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.
author
M.
Sadeghi
Department of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.
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
S.
Karimzadeh
Department of Mathematics, Vali-e-Asr University of Rafsanjan , P.O.Box 7718897111,
Rafsanjan, Iran.
author
R.
Nekooei
Department of Mathematics, Shahid Bahonar University of Kerman, P.O.Box 76169133,
Kerman, Iran.
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
A.R.
Naghipour
Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.
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
H. R.
Afshin
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
S.
Bagheri
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
M. A.
Mehrjoofard
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
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
Department of Mathematics, University of Yasouj, P.O.Box 75914, Yasouj, Iran.
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
M.
Bakhshi
Department of Mathematics, University of Bojnord, P.O.Box 1339, Bojnord, 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
A. A.
Estaji
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar,
Iran.
author
T.
Haghdadi
Faculty of Basic Sciences, Birjand University of technology Birjand, Iran.
author
J.
Farokhi Ostad
Faculty of Basic Sciences, Birjand University of technology Birjand, Iran.
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
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 87317-51167, Kashan, I. R. Iran
author
A. R.
Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 87317-51167, Kashan, I. R. Iran
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