S-Weakly Prime Ideals in Noncommutative Rings

Abstract

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)].