let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

Let X be a compact Hausdorff space, and let {Ax : x ∈ X} {Bx collections of Banach algebras such that each Ax is Bx-bimodule. Using the theory bundles spaces as tool, we investigate module amenability certain Ax-valued functions on over Bx-valued X.

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.

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

Abstract. Let (R,P) be a Noetherian unique factorization do-main (UFD) and M be a finitely generated R-module. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphi...