Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES11048210.22044/jas.2015.482ENM.AghapournahrDepartment of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-
8349, Iran.Kh.Ahmadi-amoliDepartment of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.M.SadeghiDepartment of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.Journal Article20140723We 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. <br />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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS112248310.22044/jas.2015.483ENS.KarimzadehDepartment of Mathematics, Vali-e-Asr University of Rafsanjan , P.O.Box 7718897111,
Rafsanjan, Iran.R.NekooeiDepartment of Mathematics, Shahid Bahonar University of Kerman, P.O.Box 76169133,
Kerman, Iran.Journal Article20140727In 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES233048410.22044/jas.2015.484ENA.R.NaghipourDepartment of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.0000-0002-7178-6173Journal Article20140712The 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 <br />definition, we extend the Generalized Principal Ideal Theorem to modules.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE313848610.22044/jas.2015.486ENH. R.AfshinDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.S.BagheriDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.M. A.MehrjoofardDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20150116The 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS394748710.22044/jas.2015.487ENM.BaziarDepartment of Mathematics, University of Yasouj, P.O.Box 75914, Yasouj, Iran.Journal Article20141127In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. We<br />observe that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ is<br />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<br />$Bbb{A}_*(M)neq S(M)setminus {0}$, $Bbb{A}_*(M)=emptyset$<br />if and only if $M$ is a uniform module and ann$(M)$ is a prime<br />ideal of $R$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601HvMV-ALGEBRAS II496448810.22044/jas.2015.488ENM.BakhshiDepartment of Mathematics, University of Bojnord, P.O.Box 1339, Bojnord, Iran.0000-0001-6552-1307Journal Article20140406In 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601FUZZY NEXUS OVER AN ORDINAL658248910.22044/jas.2015.489ENA. A.EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar,
Iran.0000-0001-8993-5109T.HaghdadiFaculty of Basic Sciences, Birjand University of technology Birjand, Iran.J.Farokhi OstadFaculty of Basic Sciences, Birjand University of technology Birjand, Iran.Journal Article20150207In this paper, we define fuzzy subnexuses over a nexus $N$. <br />Define and study the notions of the prime fuzzy subnexuses and the fractions<br />induced by them.<br /> Finally, we show that if S is a meet<br />closed subset of the set Fsub(N), of fuzzy subnexuses of a nexus N, and<br />h= ⋀S ϵ S, then the fractions S^-1 N and h^-1 N are isomorphic as meet-semilattices.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS889549010.22044/jas.2015.490ENM.JalaliDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 87317-51167, Kashan, I. R. IranA. R.AshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O.Box 87317-51167, Kashan, I. R. IranJournal Article20141130Suppose $G$ 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 $eta(G)$.<br />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.