Generalizations of strongly hollow ideals and a corresponding topology

Seçil Çeken; Cem Yüksel; Seçil Çeken; Cem Yüksel

doi:10.3934/math.2021751

AIMS Mathematics

2021, Volume 6, Issue 12: 12986-13003. doi: 10.3934/math.2021751

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Research article

Generalizations of strongly hollow ideals and a corresponding topology

Seçil Çeken ^,,
Cem Yüksel

Trakya University, Faculty of Science, Department of Mathematics, Edirne, Turkey

Received: 02 March 2021 Accepted: 22 August 2021 Published: 13 September 2021
MSC : 13A15, 13C05, 13C99, 13C13

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.
- strongly hollow submodule,
- pseudo strongly hollow submodule,
- M-strongly hollow ideal,
- PSH-Zariski topology
Citation: Seçil Çeken, Cem Yüksel. Generalizations of strongly hollow ideals and a corresponding topology[J]. AIMS Mathematics, 2021, 6(12): 12986-13003. doi: 10.3934/math.2021751

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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.

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