Journal of applied mathematics & informatics

  • 제42권5호
  • /
  • Pages.1171-1182
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  • 2024
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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STUDY ON S-PRIME IDEAL AS NILPOTENT IDEAL

  • C.V. MYTHILY (Department of Mathematics, Bharathiar University PG Extension and Research Centre) ;
  • D. KALAMANI (Department of Mathematics, Bharathiar University PG Extension and Research Centre)
  • 투고 : 2024.01.25
  • 심사 : 2024.05.27
  • 발행 : 2024.09.30
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초록

Let S be a multiplicative subset of a commutative ring 𝓡 with unity and Is be an S-prime ideal of 𝓡 which is disjoint from the multiplicative subset S. In this paper, some properties of the S-prime ideal, namely sum, union and intersection of two S-prime ideals are studied in a commutative ring 𝓡 with unity. It is proved that a nilradical of 𝓡 is the S-prime ideal of 𝓡. Zorn's lemma is used to state that an S-prime ideal is unique in a local ring 𝓡. Finally, the S-prime ideals in the semilocal ring are classified. The generalized S-prime ideal and its multiplicative subsets of a finite commutative ring with unity are presented.

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