Results on various derivations and Posner’s theorem in prime ideals of rings

Abdelkarim Boua; Gurninder Singh Sandhu

doi:10.5269/bspm.62478

Abdelkarim Boua Sidi Mohamed Ben Abdellah University https://orcid.org/0000-0002-6397-4713
Gurninder Singh Sandhu Patel Memorial National College https://orcid.org/0000-0001-8618-6325

Abstract

Let R be a ring and P be a prime ideal of R: In this work, we study the structure of the quotient ring R=P in a new and more general way by discussing various algebraic identities on appropriate subsets of R involving multiplicative (generalized)-(α; β)-derivations, multiplicative generalized (α; β)-derivations, multiplicative generalized derivations and generalized derivations. In addition, we give examples exhibiting the cruciality of the hypothesis of our results.

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