فهرست مطالب

Journal of Algebraic Systems
Volume:3 Issue: 1, Summer - Autumn 2015

  • تاریخ انتشار: 1395/06/11
  • تعداد عناوین: 8
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  • Moharram Aghapournahr, Khadijeh Ahmadi, Amoli, Miryousef Sadeghi Pages 1-10
    ýWe introduce a generalization of the notion ofý depth of an ideal on a module by applying the concept ofý local cohomology modules with respect to a pairý ýof idealsý. ýWe also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modulesý. ýThese kind of modules are different from Cohen- Macaulay modulesý, as an example showsý. ýAlso an artinian result for such modules is givený.
    Keywords: local cohomology modules defined by a pair of ideals_system of ideals_depth of a pair of ideals_$(I_J)$_Cohen_Macaulay modules
  • Somayeh Karimzadeh, Reza Nekooei Pages 11-22
    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.
    Keywords: Prime submodule, Integral element, Integrally closed
  • Alireza Naghipour Pages 23-30
    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.
    Keywords: Generalized Principal Ideal Theorem, Prime submodule, Completely prime submodule
  • M. A. Mehrjoofard, H. R. Afshin, S. Bagheri Pages 31-38
    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.
    Keywords: generalized projector, joint higher rank numerical range, joint matrix numerical range, joint matrix higher rank numerical range, generalized joint higher rank numerical range
  • M. Baziar Pages 39-47
    In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. We observe that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ is connected 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 prime ideal of $R$.
    Keywords: Zero, divisor graph, Annihilating submodule graph, Weakly annihilating submodule
  • Mahmood Bakhshi Pages 49-64
    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.
    Keywords: MV, algebra, HvMV, algebra, HvMV, ideal, fundamental MV, algebra
  • T. Haghdadi, A. A. Estaji, J. Farokhi Ostad Pages 65-82
    ýýIn this paperý, ýwe define fuzzy subnexuses over a nexus $N$ý. ýDefine and study the notions of the prime fuzzy subnexuses and the fractionsý ýinduced by themý. ýFinallyý, ýwe show that if S is a meetý ýclosed subset of the set Fsub(N), ýof fuzzy subnexuses of a nexus Ný, ýandý ýh= ⋀S ϵ S, ýthen the fractions S^-1 N and h^-1 N are isomorphic as meet-semilatticesý.
    Keywords: ýNexusý_ýordinalý_ýPrime fuzzy subnexusý_ýFractioný ýof a nexusý
  • M. Jalali, Rad, A. R. Ashrafi Pages 83-95
    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 $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{ n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of order $4p$ or $p^3$, where $p$ and $q$ are primes.
    Keywords: Conjugacy class, normal subset, $p, $group