Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES1916910.22044/jas.2013.169ENMoharram AghapournahrArak AniversityJournal Article20130630Let $R$ be a commutative Noetherian ring with non-zero identity and <br />$fa$ an ideal of $R$. Let $M$ be a finite $R$--module <br />of finite projective dimension and $N$ an arbitrary finite $R$--module. <br />We characterize the membership of the generalized local cohomology modules <br />$lc^{i}_{fa}(M,N)$ in certain Serre <br />subcategories of the category of modules from upper bounds. We define and study <br />the properties of a generalization of cohomological dimension of generalized local <br />cohomology modules. Let $mathcal S$ be a Serre subcategory of the category <br />of $R$--modules and $n > pd M$ be an integer such that $lc^{i}_{fa}(M,N)$ <br /> belongs to $mathcal S$ for all $i> n$. Then, for any ideal $fbsupseteq fa$, it is also <br /> shown that the module <br /> $lc^{n}_{fa}(M,N)/{fb}lc^{n}_{fa}(M,N)$ belongs to $mathcal S$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS113116710.22044/jas.2013.167ENL. Kamali ArdakaniYazd UniversityBijan DavvazYazd UniversityJournal 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.2013.166ENMahdieh HaddadiDepartment of Mathematics, Faculty of Mathematics, Statistics and computer science, Semnan University, Semnan, Iran.Journal Article20130305Nets, useful topological tools, used to generalize certain<br />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<br />poset with an action of a posemigroup $S$ on it which<br />is a very useful structure in computer sciences and interesting<br />for mathematicians, and give the the concept of $S$-net. Using $S$-nets and its<br />convergency we also give some characterizations of separated<br />$S$-posets.<br /><br />Also, introducing the net-closure operators, we investigate<br />the counterparts of topological separation axioms on $S$-posets<br />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.2013.165ENHanieh MirebrahimiDepartment of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, IranFatemeh GhaneiDepartment 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 $mathbb{Z}_{m}*mathbb{Z}_{n}$ 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.2013.164ENMohammad ArashiDepartment 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 orthogonal transformations.Shahrood University of TechnologyJournal of Algebraic Systems2345-51281120130915GENERALIZATIONS OF delta-LIFTING MODULES677716810.22044/jas.2013.168ENYahya TalebiUniversity of Mazandaran, BabolsarMehrab HosseinpourUniversity of MazandaranJournal Article20130406In this paper we introduce the notions of G∗L-module and G∗L-module which<br /><br />are two proper generalizations of δ-lifting modules. We give some characteriza tions and <br />properties of these modules. We show that a G∗L-module decomposes<br />into a semisimple submodule M1 and a submodule M2 of M such that every non-zero submodule of M2 <br />contains a non-zero δ-cosingular submodule.