The Zariski topology on the secondary like spectrum of a module

Abstract

Let $R$ be a commutative ring with unity and $M$ be a left $R$-module. We define the secondary-like spectrum of $M$ to be the set of all secondary submodules $K$ of $M$ such that $An{n}_R(soc(K))=\sqrt{An{n}_R(K)}$, and we denote it by $Spe{c}^L(M)$. In this paper, we introduce a topology on $Spe{c}^L(M)$ having the Zariski topology on the second spectrum $Spe{c}^s(M)$ as a subspace topology, and study several topological structures of this topology.

References in corpus (1)

• Graded modules with Noetherian graded second spectrum