2015
3
1
1
95
THE CONCEPT OF (I; J)COHEN MACAULAY MODULES
2
2
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 $(I,J)$CohenMacaulay modules as a generalization of concept of CohenMacaulay modules. These kind of modules are different from CohenMacaulay modules, as an example shows. Also an artinian result for such modules is given.
1

1
10


M.
Aghapournahr
Department of Mathematics, Faculty of Science, Arak University, Arak, 381568
8349, Iran.
Department of Mathematics, Faculty of Science,
Iran
m.aghapour@gmail.com


Kh.
Ahmadiamoli
Department of Mathematics, Payame Noor University, Tehran, 193953697, Iran.
Department of Mathematics, Payame Noor University,
Iran
khahmadi@pnu.ac.ir


M.
Sadeghi
Department of Mathematics, Payame Noor University, Tehran, 193953697, Iran.
Department of Mathematics, Payame Noor University,
Iran
m.sadeghi@phd.pnu.ac.ir
local cohomology modules defined by a pair of ideals
system of ideals
depth of a pair of ideals
$(I
J)$CohenMacaulay modules
AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS
2
2
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.
1

11
22


S.
Karimzadeh
Department of Mathematics, ValieAsr University of Rafsanjan , P.O.Box 7718897111,
Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
karimzadeh_s@yahoo.com


R.
Nekooei
Department of Mathematics, Shahid Bahonar University of Kerman, P.O.Box 76169133,
Kerman, Iran.
Department of Mathematics, Shahid Bahonar
Iran
rnekooei@uk.ac.ir
Prime submodule
Integral element
Integrally closed
GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
2
2
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an Rmodule 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.
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23
30


A.R.
Naghipour
Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.
Department of Mathematical Sciences, Shahrekord
Iran
naghipourar@yahoo.com
Generalized Principal Ideal Theorem
Prime submodule
Completely prime submodule
GENERALIZED JOINT HIGHERRANK NUMERICAL RANGE
2
2
The rankk 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 rankk numerical range is nonempty. In this paper the notion of joint rankk numerical range is generalized and some statements of [2011, Generalized numerical ranges and quantum error correction, J. Operator Theory, 66: 2, 335351.] are extended.
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31
38


H. R.
Afshin
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
hamidrezaafshin@yahoo.com


S.
Bagheri
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
bagherisedighe@yahoo.com


M. A.
Mehrjoofard
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
aahaay@gmail.com
generalized projector
joint higher rank numerical range
joint matrix numerical range
joint matrix higher rank numerical range
generalized joint higher rank numerical range
ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS
2
2
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 $R$.
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39
47


M.
Baziar
Department of Mathematics, University of Yasouj, P.O.Box 75914, Yasouj, Iran.
Department of Mathematics, University of
Iran
mbaziar@yu.ac.ir
zerodivisor graph
Annihilating submodule graph
Weakly annihilating submodule
HvMVALGEBRAS II
2
2
In this paper, we continue our study on HvMValgebras. The quotient structure of an HvMValgebra 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 HvMValgebra and the direct product of a family of HvMValgebras are investigated and some related results are obtained.
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49
64


M.
Bakhshi
Department of Mathematics, University of Bojnord, P.O.Box 1339, Bojnord, Iran.
Department of Mathematics, University of
Iran
bakhshi@ub.ac.ir
MValgebra
HvMValgebra
HvMVideal
fundamental MValgebra
FUZZY NEXUS OVER AN ORDINAL
2
2
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 meetsemilattices.
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65
82


A. A.
Estaji
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar,
Iran.
Faculty of Mathematics and Computer Sciences,
Iran
aaestaji@hsu.ac.ir


T.
Haghdadi
Faculty of Basic Sciences, Birjand University of technology Birjand, Iran.
Faculty of Basic Sciences, Birjand University
Iran
t.haghdady@gmail.com


J.
Farokhi Ostad
Faculty of Basic Sciences, Birjand University of technology Birjand, Iran.
Faculty of Basic Sciences, Birjand University
Iran
javadfarrokhi90@gmail.com
Nexus
ordinal
Prime fuzzy subnexus
Fraction of a nexus
COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
2
2
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.
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88
95


M.
Jalali
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 8731751167, Kashan, I. R. Iran
Department of Pure Mathematics, Faculty of
Iran
jalali6834@gmail.com


A. R.
Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 8731751167, Kashan, I. R. Iran
Department of Pure Mathematics, Faculty of
Iran
ashrafi@kashanu.ac.ir
Conjugacy class
normal subset
$p$group