More on S-pseudo radical of an ideal and a new class of ideals in noncommutative rings
Communications in Algebra, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/00927872.2026.2723319
- Dergi Adı: Communications in Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: noncommutative rings, S-prime ideals, S-principally-nilary ideals, S-pseudo radical, S-radical ideals, SS-primary ideals
- Çukurova Üniversitesi Adresli: Evet
Özet
We further develop the theory of the (Formula presented.) -pseudo radical (Formula presented.) of ideals in noncommutative rings and introduce a new class of ideals, called right (Formula presented.) -primary ideals. We establish the compatibility of (Formula presented.) with ring epimorphisms and provide explicit descriptions in idealization rings, direct products, and matrix rings. We also revisit (Formula presented.) -principally-nilary ideals, relating them to elementwise and ideal-theoretic (Formula presented.) -pseudo-radical conditions and obtaining equivalent characterizations under a finite-generation hypothesis. Finally, we study the behavior of right (Formula presented.) -primary ideals under standard ring constructions and compare them with right (Formula presented.) -prime ideals. Examples show that these two notions are generally incomparable. They are equivalent for (Formula presented.) -radical ideals, while in a fully idempotent ring, finite generation of (Formula presented.) ensures that every right (Formula presented.) -primary ideal (Formula presented.) is right (Formula presented.) -prime.