$S$-weakly prime ideals in noncommutative rings

Authors

  • Hatice Çay IMU Vocational School, Istanbul Medipol University and Department of Mathematics, Yıldız Technical University, Istanbul, Turkey)
  • Bayram Ali Ersoy Department of Mathematics, Yıldız Technical University, Istanbul, Turkey

DOI:

https://doi.org/10.3842/umzh.v77i5.8391

Keywords:

noncommutative rings, s-prime ideals, s-weakly prime ideals, weakly prime ideals

Abstract

UDC 512.5

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)].

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 5, 2025.

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Published

23.07.2025

Issue

Vol. 77 No. 5 (2025)

Section

Research articles