Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POSNER'S THEOREM FOR GENERALIZED DERIVATIONS ASSOCIATED WITH A MULTIPLICATIVE DERIVATION

  • UZMA NAAZ (Department of Mathematics & Statistics, Integral University) ;
  • MALIK RASHID JAMAL (Department of Mathematics & Statistics, Integral University)
  • Received : 2023.09.19
  • Accepted : 2024.03.19
  • Published : 2024.05.30
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Abstract

Let R be a ring and P be a prime ideal of R. A mapping d : R → R is called a multiplicative derivation if d(xy) = d(x)y + xd(y) for all x, y ∈ R. In this paper, our main motive is to obtain the well-known theorem due to Posner in the ring R/P for generalized derivations associated with a multiplicative derivation defined by an additive mapping F : R → R such that F(xy) = F(x)y + xd(y), where d : R → R is a multiplicative derivation not necessarily additive. This article discusses the use of generalized derivations associated with a multiplicative derivation to investigate the commutativity of the quotient ring R/P.

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Acknowledgement

The authors are grateful to the referees for their valuable suggestions and remarks that definitely improved the paper. The authors would like to thank Integral University, Lucknow, for providing the manuscript communication number IU/R & D/2023-MCN 0002188 for the present work.

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