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


Moharram
Aghapournahr
Arak Aniversity
Arak Aniversity
Iran
m.aghapour@gmail.com


Khadijeh
Ahmadiamoli
Payame Noor University, Tehran
Payame Noor University, Tehran
Iran
khahmadi@pnu.ac.ir


Miryousef
Sadeghi
Payame Noor University, Tehran
Payame Noor University, Tehran
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


Somayeh
Karimzadeh
ValieAsr university of Rafsanjan
ValieAsr university of Rafsanjan
Iran
karimzadeh_s@yahoo.com


Reza
Nekooei
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
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.
1

23
30


Alireza
Naghipour
Shahrekord University,
Shahrekord University,
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.
1

31
38


M. A.
Mehrjoofard
Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Mathematics, Faculty of Mathematics
Iran
aahaay@gmail.com


H. R.
Afshin
department of mathematics,
ValieAsr University of Rafsanjan, Iran
department of mathematics,
ValieAsr University
Iran
hamidrezaafshin@yahoo.com


S.
Bagheri
department of mathematics, ValieAsr University of Rafsanjan
department of mathematics, ValieAsr University
Iran
bagherisedighe@yahoo.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 $R$.
1

39
47


M.
Baziar
Yasouj University
Yasouj University
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.
1

49
64


mahmood
bakhshi
teacher.bojnoord university.iran
teacher.bojnoord university.iran
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.
1

65
82


T.
Haghdadi
Birjand University of Technology
Birjand University of Technology
Iran
t.haghdady@gmail.com


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


J.
Farokhi Ostad
Faculty of Basic Sciences, Birjand University of technology
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.
1

88
95


M.
JalaliRad
University of Kashan
University of Kashan
Iran
jalali6834@gmail.com


A. R.
Ashrafi
University of Kashan
University of Kashan
Iran
ashrafi@kashanu.ac.ir
Conjugacy class
normal subset
$p$group