Some identities in quotient rings

Mouhamadi El Hamdaoui; Abdelkarim Boua; Gurninder S. Sandhu

doi:10.5269/bspm.62481

Mouhamadi El Hamdaoui Sidi Mohamed Ben Abdellah University
Abdelkarim Boua Sidi Mohamed Ben Abdellah University
Gurninder S. Sandhu Patel Memorial National College https://orcid.org/0000-0001-8618-6325

Abstract

Let R be an associative ring, P a prime ideal of R: In this paper, we study the structure of the ring R=P and describe the possible forms of the generalized derivations satisfying certain algebraic identities on R: As a consequence of our theorems, we first investigate strong commutativity preserving generalized derivations of prime rings, and then examine the generalized derivations acting as (anti)homomorphisms in prime rings. Some commutativity theorems also given in semi-prime rings.

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