Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES1916910.22044/jas.2013.169ENMoharramAghapournahrDepartment of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.Journal Article20130630Let $R$ be a commutative Noetherian ring with non-zero identity and $a$ an ideal of $R$. Let $M$ be a finite $R$--module<br />of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $H^{i}_{a}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $H^{i}_{a}(M,N)$ belongs to $mathcal S$ for all $i> n$. Then, for any ideal $bsupseteq a$, it is also shown that the module $H^{n}_{a}(M,N)/{b}H^{n}_{a}(M,N)$ belongs to $mathcal S$.<br /><br />Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS113116710.22044/jas.2013.167ENL.Kamali ArdakaniDepartment of Mathematics, Yazd University, Yazd, Iran.BijanDavvazDepartment of Mathematics, Yazd University, Yazd, Iran.Journal Article20130311Recently, the algebraic theory of MV -algebras is intensively studied. <br />In this paper, we extend the concept of derivation of $MV$-algebras and we give some<br />illustrative examples. Moreover, as a generalization of derivations of $MV$ -algebras<br />we introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.<br />Also, we investigate some properties of them.Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915NETS AND SEPARATED S-POSETS334316610.22044/jas.2013.166ENMahdiehHaddadiDepartment of Mathematics, Faculty of Mathematics, Statistics and computer science, Semnan University, Semnan, Iran.Journal Article20130305Nets, useful topological tools, used to generalize certain concepts that may only be general enough in the context of metric<br />spaces. In this work we introduce this concept in an $S$-poset, a poset with an action of a posemigroup $S$ on it which<br />is a very useful structure in computer sciences and interesting for mathematicians, and give the the concept of $S$-net. Using $S$-nets and its convergency we also give some characterizations of separated $S$-posets. Also, introducing the net-closure operators, we investigate the counterparts of topological separation axioms on $S$-posets and study their relation to separated $S$-posets.Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES455216510.22044/jas.2013.165ENHaniehMirebrahimiDepartment of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, IranFatemehGhaneiDepartment of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, IranJournal Article20130301In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of ${Z}_{m}*{Z}_{n}$ is free of rank $(m-1)(n-1)$ for all $m,ngeq2$Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915ON SELBERG-TYPE SQUARE MATRICES INTEGRALS536516410.22044/jas.2013.164ENMohammadArashiDepartment of Statistics
School of Mathematics,
Shahrood University of Technology,
Shahrood, Iran.Journal Article20130226In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under<br />orthogonal transformations.Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915GENERALIZATIONS OF δ-LIFTING MODULES677716810.22044/jas.2013.168ENYahyaTalebiDepartment of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, IranMehrabHosseinpourDepartment of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, IranJournal Article20130406In this paper we introduce the notions of $G_{1}^{*}L$-module and $G_{2}^{*}L$-module which are two proper generalizations of $delta$-lifting modules. We give some characterizations and properties of these modules. We show that a<br />$G_{2}^{*}L$-module decomposes into a semisimple submodule $M_{1}$ and a submodule $M_{2}$ of $M$ such that every non-zero submodule of $M_{2}$ contains a non-zero $delta$-cosingular submodule.