On derivations and semiprime ideal of rings

2025/02/25 by Sandhu, Gurninder Singh, Rehman, Nadeem Ur
#16N60 #16W25 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2502.17965

Abstract

Let R be an associative ring with a nonzero ideal I and a semiprime ideal T such that T\subsetneq I. Let K be a nonempty subset of R and d:R→ R be a derivation of R, if [d(x),x]∈ T for all x∈ K, then d is said to be a T-commuting derivation on K. We show that if some specific T-valued differential identities are imposed on I, then d is T-commuting. Moreover, we provide semiprime ideal variant of some known results on derivations.

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