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

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.