Generalizations of strongly hollow ideals and a corresponding topology

Abstract

In this paper, we introduce and study the notions of $ M $-strongly hollow and $ M $-PS-hollow ideals where $ M $ is a module over a commutative ring $ R $. These notions are generalizations of strongly hollow ideals. We investigate some properties and characterizations of $ M $-strongly hollow ($ M $-PS-hollow) ideals. Then we define and study a topology on the set of all $ M $-PS-hollow ideals of a commutative ring $ R $. We investigate when this topological space is irreducible, Noetherian, $ T_{0} $, $ T_{1} $ and spectral space.

Keywords

• strongly hollow submodule
• pseudo strongly hollow submodule
• m-strongly hollow ideal
• psh-zariski topology