Open AccessGeneralizations of strongly hollow ideals and a corresponding topology
Author(s) -
Seçil Çeken,
Cem Yüksel
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021751
Subject(s) - commutative property , mathematics , noetherian , noetherian ring , topology (electrical circuits) , commutative ring , space (punctuation) , pure mathematics , ring (chemistry) , spectral space , discrete mathematics , combinatorics , algebra over a field , computer science , chemistry , organic chemistry , operating system
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.