S-weakly prime ideals in noncommutative rings

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Çay H., Ersoy B. A.

UKRAINIAN MATHEMATICAL JOURNAL, vol.77, no.5, pp.369-370, 2025 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 77 Issue: 5
  • Publication Date: 2025
  • Doi Number: 10.3842/umzh.v77i5.8391
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.369-370
  • Istanbul Medipol University Affiliated: Yes

Abstract

Let  be a noncommutative ring.  The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, 28, 43–68 (2020)]), were devoted to the investigation of weakly prime ideals in  noncommutative rings. In this work, we generalize  their findings by introducing the concept of -weakly prime ideals via taking  as an -system, which is also a generalization of the concept of right -prime ideals first introduced in [Mediterran.  J. Math., 21, No. 2, Article 43 (2024)].