S-VERSIONS AND S-GENERALIZATIONS OF IDEMPOTENTS, PURE IDEALS AND STONE TYPE THEOREMS

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of...

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Published in:Taehan Suhakhoe hoebo 2024, Vol.61 (1), p.83-92
Main Authors: Bayram Ali Ersoy, Unsal Tekir, Eda Yildiz
Format: Article
Language:Korean
Online Access:Get full text
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Summary:Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is S-pure but the converse may not be true. Afterwards, we show that there is a relation between S-pure ideals of R and closed sets of S-Zariski topology that are stable under generalization.
ISSN:1015-8634