S-weakly prime ideals in noncommutative rings - Çay, Hatice; Ersoy, Bayram Ali (Ukrains’kyi Matematychnyi Zhurnal, 2025)
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)].