Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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S-VERSIONS AND S-GENERALIZATIONS OF IDEMPOTENTS, PURE IDEALS AND STONE TYPE THEOREMS

  • Bayram Ali Ersoy (Department of Mathematics Yildiz Technical University) ;
  • Unsal Tekir (Department of Mathematics Marmara University) ;
  • Eda Yildiz (Department of Mathematics Yildiz Technical University)
  • Received : 2023.01.11
  • Accepted : 2023.05.09
  • Published : 2024.01.31
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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.

Keywords

Acknowledgement

The authors acknowledge Prof. Dr. Abolfazl Tarizadeh for his helpful comments on the paper. Also we would like to thank the referee for his/her comments and corrections.

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