Journal of Algebraic Systems
Volume:3 Issue: 2, Winter - Spring 2016

The purpose of this article is to develop the notions of amenability for vector valued group algebras. We prove that L1(G, A) is approximately weakly amenable where A is a unital separable Banach algebra. We give necessary and sufficient conditions for the existence of a left invariant mean on L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

In 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) 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.

Let 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.

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standard graded ring, $M$ be a finitely generated graded $R$-module and $J$ be a homogenous ideal of $R$. In this paper we study the graded structure of the $i$-th local cohomology module of $M$ defined by a pair of ideals $(R_{},J)$, i.e. $H^{i}_{R_{},J}(M)$. More precisely, we discuss finiteness property and vanishing of the graded components $H^{i}_{R_{},J}(M)_{n}$. Also, we study the Artinian property and tameness of certain submodules and quotient modules of $H^{i}_{R_{},J}(M)$.

Let $(R,\underline{m})$ 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.

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.
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.

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$" , $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namely left $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magma if and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$ join law holds. Right (and two-sided) magma-$e$-magmas are defined in an analogous way.Also, $X$ is magma-joined-magma if it is magma-$x$-magma, for all $xin X$. Therefore, we introduce a big class of basic algebraic structures with two binary operations which some of their sub-classes are group-$e$-semigroups, loop-$e$-semigroups, semigroup-$e$-quasigroups, etc. A nice infinite [resp. finite] example for them is real group-grouplike $(mathb {R},, ,_1)$ [resp. Klein group-grouplike]. In this paper, I introduce and study the topic, construct several big classes of such algebraic structures and characterize all identical magma-$e$-magma in several ways. The motivation of this study lies in some interesting connections to $f$-Multiplications, some basic functional equations on algebraic structures and Grouplikes (recently been introduced by the author). At last, we show some of future directions for the researches.

In 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.

Let $(R,fm)$ be a Gorenstein local ring and $M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are in the same even liaison class, then one has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.

Let $R$ be a commutative Noetherian ring, $fa$ an ideal of $R$ and $mathcal{D}(R)$ denote the derived category of $R$-modules. For any homologically bounded complex $X$, we conjecture that $sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove this in several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.