대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권1호
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  • Pages.83-92
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  • 2024
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2023.01.11
  • 심사 : 2023.05.09
  • 발행 : 2024.01.31
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초록

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.

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과제정보

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.

참고문헌

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