Akademik Veri Yönetim Sistemi
Bollettino dell'Unione Matematica Italiana, 2026 (ESCI, Scopus)
This paper presents a comprehensive study of right S-maximal ideals in noncommutative rings, providing a natural extension of classical ideal theory through the framework of m-systems. We establish deep connections among right S-maximal, S-comaximal, and S-prime ideals, and introduce new concepts such as the S-Jacobson radical and S-invertible elements to further develop the structural theory of rings. A key contribution is the introduction of S-local rings and the formulation of an S-version of Nakayama’s Lemma. In addition, we propose two complementary definitions of left S-primitive ideals–one ideal-theoretic and the other annihilator-based–and demonstrate their intrinsic relationship to S-prime ideals. Our results not only unify and generalize existing notions but also open promising avenues for further research, particularly in exploring the interplay between different forms of S-primitivity.