Differential identities and S -Jordan derivations over S -prime and S -semiprime rings

2025/12/22 by Brahim Mahdou, Brahim Boudine
Mathematics · Decision Sciences · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory

paper · doi:10.1080/00927872.2025.2598665

Abstract

Let R be an associative ring and S be a multiplicatively closed set in R. In this paper, we introduce S-prime rings, S-semiprime rings, S-derivations and S-Jordan derivations. First, we extend Posner’s theorem and Herstein’s theorem to S-prime rings. Assuming S⊆Z(R), we prove that every S-Jordan derivation on an S-prime or S-semiprime ring is an S-derivation.

Citations

• S-NOETHERIAN RINGS
• Derivations in prime rings
• Certain algebraic identities on prime rings with involution

Related

• On Semiprime Rings with (α,α)-Symmetric Derivations
• On derivations and semiprime ideal of rings
• Generalized Jordan derivations on semiprime rings
• Generalized (m,n)-Jordan centralizers and derivations on semiprime rings
• On Generalized (m, n)-Jordan Derivations and Centralizers of Semiprime Rings