Shahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901MOST RESULTS ON A-IDEALS IN MV -MODULES11399410.22044/jas.2017.994ENS. Saidi GoraghaniDepartment of Mathematics, University of Farhangian, Tehran, Iran.R. A. BorzooeiDepartment of Mathematics, University of Shahid Beheshti, Tehran, Iran.0000-0001-7538-7885Journal Article20160218In the present paper, by considering the notion of<br /> MV-modules which is the structure that naturally correspond<br /> to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $K\subseteq \bigcup _{i=1}^{n}K_{i}$ implies $K\subseteq K_{j}$, where $K,K_{1},\cdots ,K_{n}$ are A-ideals of A-module M and $1\leq j\leq n$.https://jas.shahroodut.ac.ir/article_994_dd6f0758634fc1dfcc2fb67c9d67677e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901AN INDUCTIVE FUZZY DIMENSION152599510.22044/jas.2017.995ENM. AbrySchool of Mathematics and Computer Science, University of Damghan, P.O. Box
3671641167, Damghan, Iran.Jafar ZanjaniSchool of Mathematics and Computer science, University of Damghan, P.O.Box 3671641167, Damghan, Iran.Journal Article20160403Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are established.https://jas.shahroodut.ac.ir/article_995_5557c9774af984cbc69e62c98e4c2f2a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901TABLE OF MARKS OF FINITE GROUPS275199610.22044/jas.2017.996ENM. GhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785{136, I. R. IranF. AbbasiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785{136, I. R. IranJournal Article20160619Let G be a finite group and C(G) be the family of representative conjugacy classes of<br /> subgroups of G. The matrix whose H;K-entry is the number of fixed points of the set<br /> G=K under the action of H is called the table of marks of G where H;K run through all<br /> elements in C(G). In this paper, we compute the table of marks and the markaracter table<br /> of groups of order pqr where p, q, r are prime numbers.https://jas.shahroodut.ac.ir/article_996_a1fbc5e498c184e7f032d12626d80c2e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901GENERALIZED GORENSTEIN DIMENSION OVER GROUP RINGS536499710.22044/jas.2017.997ENAbdolnaser BahlekehDepartment of Mathematics, Gonbad Kavous University, P.O. Box 4971799151,
Gonbad Kavous, Iran.T. KakaieDepartment of Mathematics, University of Isfahan, P.O. Box: 81746-73441, Isfa-
han, Iran.Journal Article20161221Let $(R, \m)$ be a commutative noetherian local ring and let $\Gamma$ be a finite group.<br /> It is proved that if $R$ admits a dualizing module, then the group ring $R\ga$ has a<br /> dualizing bimodule as well. Moreover, it is shown that a finitely generated $R\ga$-module $M$ has generalized<br /> Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero<br /> as an $R$-module.https://jas.shahroodut.ac.ir/article_997_21bc08b517c81172cdbfcee37f64093c.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES657299810.22044/jas.2017.998ENH. R. DorbidiDepartment of Mathematics, Faculty of Science, University of Jiroft, P.O. Box
78671-61167, Jiroft, Iran.Journal Article20161108In this paper we study almost uniserial rings and modules.<br /> An R−module M is called almost uniserial if any two nonisomorphic<br /> submodules are linearly ordered by inclusion. A ring<br /> R is an almost left uniserial ring if R_R is almost uniserial. We give<br /> some necessary and sufficient condition for an Artinian ring to be<br /> almost left uniserial.https://jas.shahroodut.ac.ir/article_998_50b733a4cdef7a3d8368c4489791fda6.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901ON THE MAXIMAL SPECTRUM OF A MODULE738499910.22044/jas.2017.999ENH. Ansari-ToroghyDepartment of Pure Mathematics, Faculty of Mathematical Science, University of
Guilan, P.O. Box 41335-19141, Rasht, Iran.S. KeyvaniDepartment of Mathematics, Bandar Anzali Branch, Islamic Azad University, Ban-
dar Anzali, Iran.Journal Article20161219Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $\mbox{Max}$-injective and $\mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.https://jas.shahroodut.ac.ir/article_999_cfe480525b3eeb4d299ad10c3f1a4a16.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51285120170901A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS859088210.22044/jas.2017.882ENSeyed H. JafariDepartment of Mathematics, Shahrood University of Technology, P.O. Box
3619995161-316, Shahrood, Iran.Journal Article20150314The commuting graph of a group is a graph with vertexes set of a subset of a group and two<br /> element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting<br /> graph of a conjugacy class in the symmetric groups. The clique number, coloring number,<br /> independent number, and diameter of these graphs are also computed.https://jas.shahroodut.ac.ir/article_882_47d09a8a2984aa2088d6a1c7f4a6b771.pdf