The structure of S-semiprime ideals and submodules in noncommutative rings

Abouhalaka A., Groenewald N.

Communications in Algebra, vol.53, no.12, pp.5315-5327, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 12
  • Publication Date: 2025
  • Doi Number: 10.1080/00927872.2025.2509830
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5315-5327
  • Keywords: Prime ideals, S-prime submodules, S-pseudo radical, S-semiprime ideals, S-semiprime submodules, semiprime ideals
  • Çukurova University Affiliated: Yes

Abstract

This paper introduces the concept of right S-semiprime ideals and right S-semiprime submodules in the context of noncommutative rings. We investigate the properties of right S-semiprime ideals (submodules), providing multiple equivalent definitions and exploring their relationship with classical semiprime ideals (submodules). Key results include the definitions and characterizations of S-radical and S-pseudo radical concepts for ideals. The paper concludes with new insights into the structure of right S-semiprime submodules.