On the Prime Spectrum of Torsion Modules

A scheme over quasi-prime spectrum of modules

The notions of quasi-prime submodules and developed  Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...

L-Prime Spectrum of Modules

We investigate the Zariski Topology on the L-prime spectrum of modules consisting of the collection of all prime Lsubmodules and prove some useful results.

Zariski-Like Topology on the Classical Prime Spectrum of a Modules

Asymptotic Prime Divisors of Torsion-free Symmetric Powers of Modules

Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).

on direct sums of baer modules

the notion of baer modules was defined recently

zariski-like topology on the classical prime spectrum of a modules