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<p>Let <i>R</i> be a noncommutative ring. The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., <b>47</b>, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, <b>28</b>, 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 <i>S</i>-weakly prime ideals via taking <i>S</i> as an <i>m</i>-system, which is also a generalization of the concept of right <i>S</i>-prime ideals first introduced in [Mediterran. J. Math., <b>21</b>, No. 2, Article 43 (2024)].</p>

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S-Weakly Prime Ideals in Noncommutative Rings

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Hatice Çay,
  • Bayram Ali Ersoy

摘要

Let R 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 S-weakly prime ideals via taking S as an m-system, which is also a generalization of the concept of right S-prime ideals first introduced in [Mediterran. J. Math., 21, No. 2, Article 43 (2024)].