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

ERSOY B. A., TEKİR Ü., YILDIZ E.

Bulletin of the Korean Mathematical Society, vol.61, no.1, pp.83-92, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.4134/bkms.b230023
  • Journal Name: Bulletin of the Korean Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.83-92
  • Keywords: Prime spectrum, pure ideal, S-idempotent, S-Zariski topology, Stone type theorem, Zariski topology
  • Yıldız Technical University Affiliated: Yes

Abstract

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.