In this paper, we investigate the structure of derivations over trivial extensions. We provide a detailed analysis of the structure of derivations on trivial extensions, the centre of trivial extensions, and the conditions for a trivial extension to be prime. Additionally, we examine the structure of derivations on trivial extensions when the underlying ring, R, is a prime ring, under the conditions of Herstein's Theorem, Posner's Theorem, and Bell's theorem.
No takes yet. Share an insight, caveat, or question.
Boudine et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: