On derivations over trivial extensions
DOI:
https://doi.org/10.22199/issn.0717-6279-6040Keywords:
Derivation, trivial extension, prime ringAbstract
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.References
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