Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220151001AMENABILITY OF VECTOR VALUED GROUP ALGEBRAS9710761010.22044/jas.2015.610ENAli GhaffariDepartment of Mathematics, Semnan University, Semnan, IranSeyedeh Samaneh Javadi SyahkaleFaculty of Engineering- East Guilan, University of Guilan, Rudsar, IranJournal Article20140419The purpose of this article is to develop the notions of amenability<br />for vector valued group algebras. We prove that L1(G, A) is approximately<br />weakly amenable where A is a unital separable Banach algebra. We give<br />necessary and sufficient conditions for the existence of a left invariant mean<br />on L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101IDEALS IN EL-SEMIHYPERGROUPS ASSOCIATED TO ORDERED SEMIGROUPS10912561110.22044/jas.2015.611ENS. H. GhazaviDepartment of Mathematics-Yazd University-Yazd-IranS. M. AnvariyehDepartment Of Mathematics-Yazd University-Yazd-IranS. MirvakiliDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20150130In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal)<br /> of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially ordered $Gamma$-semigroup.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101ON ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE CENTER ELEMENTWISE12713161210.22044/jas.2015.612ENZahra Kaboutari FarimaniDepartment of Mathematics, University of Birjand, Birjand, Iran.Mohammad Mehdi NasrabadiDepartment of Mathematics, University of Birjand, Birjand, Iran.Journal Article20150228Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. In this paper we give necessary and sufficient condition on G such that each absolute central automorphism of G fixes the centre element-wise. Also we classify all groups of orders p^3 and p^4 whose absolute central automorphisms fix the centre element-wise.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS13314661310.22044/jas.2015.613ENMaryam JahangiriFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran,
Iran AND Institute for Research in Fundamental Sciences (IPM) P.O.Box: 19395-
5746, Tehran, Iran.Zohreh HabibbiDepartment of Mathematics, University of Payame Noor, P.O.Box 19395-3697,
Tehran, Iran.Journal Article20150414Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standard<br />graded ring, $M$ be a finitely generated graded $R$-module and $J$<br />be a homogenous ideal of $R$. In this paper we study the graded<br />structure of the $i$-th local cohomology module of $M$ defined by a<br />pair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. More<br />precisely, we discuss finiteness property and vanishing of the<br />graded components $H^{i}_{R_{+},J}(M)_{n}$.<br /><br />Also, we study the Artinian property and tameness of certain<br />submodules and quotient modules of $H^{i}_{R_{+},J}(M)$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101RESULTS ON ALMOST COHEN-MACAULAY MODULES14715061410.22044/jas.2015.614ENA. MafiDepartment of Mathematics, University of Kurdistan, P.O.Box 416, Sanandaj,
Iran.S. TabejamaatDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697,
Tehran, Iran.Journal Article20150805Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101RATIONAL CHARACTER TABLE OF SOME FINITE GROUPS15116961510.22044/jas.2015.615ENH. ShabaniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, Kashan 87317−51167, I. R. Iran.A. R. AshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, Kashan 87317−51167, I. R. Iran.M. GhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785 - 136, I. R. Iran.Journal Article20150108The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.<br />The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES17119961610.22044/jas.2015.616ENM. H. HooshmandYoung Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz,
Iran.Journal Article20150311By left magma-$e$-magma, I mean a set containing<br />the fixed element $e$, and equipped by two binary operations "$cdot$"<br />, $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namely<br />left $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magma<br />if and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.<br />Right (and two-sided) magma-$e$-magmas are defined in an analogous way.<br />Also, $X$ is magma-joined-magma if it is magma-$x$-magma, for all $xin X$. Therefore, we introduce a big class of basic<br />algebraic structures with two binary operations which some of their<br />sub-classes are group-$e$-semigroups, loop-$e$-semigroups, semigroup-$e$-quasigroups,<br />etc. A nice infinite [resp. finite] example for them is real group-grouplike $(mathbb{R},+,0,+_1)$ [resp. Klein group-grouplike].<br />In this paper, I introduce and study the topic, construct several big classes of such algebraic structures and characterize<br />all identical magma-$e$-magma in several ways. The motivation of this study lies in some<br /> interesting connections to $f$-Multiplications, some basic functional equations<br /> on algebraic structures and Grouplikes (recently been introduced by the author). At last, we show some of future directions<br />for the researches.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS20121061810.22044/jas.2015.618ENA. Yousefian DaraniDepartment of Mathematics and Applications, University of Mohaghegh Ardabili,
P.O.Box 5619911367, Ardabil, Iran.Journal Article20150808In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modules are also true for Nonnil-Noetherian modules.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101A SHORT PROOF OF A RESULT OF NAGEL21121561910.22044/jas.2015.619ENN. ShirmohammadiDepartment of Mathematics, University of Tabriz, P.O.Box 51666-16471, Tabriz,
Iran.Journal Article20150824Let $(R,fm)$ be a Gorenstein local ring and<br />$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are in<br />the same even liaison class, then<br />one has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.Shahrood University of TechnologyJournal of Algebraic Systems2345-51283220150101ON THE VANISHING OF DERIVED LOCAL HOMOLOGY MODULES21722562010.22044/jas.2015.620ENM. HatamkhaniDepartment of Mathematics,
Faculty of Science,
Arak University,
Arak, 38156-8-8349, Iran.Journal Article20150923Let $R$ be a commutative Noetherian ring, $fa$ an<br />ideal of $R$ and $mathcal{D}(R)$ denote the derived category of<br />$R$-modules. For any homologically bounded complex $X$, we conjecture that<br />$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove this<br />in several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.