Aequationes mathematicae

, Volume 86, Issue 1, pp 65–79

On multiplicative (generalized)-derivations in prime and semiprime rings

Article

DOI: 10.1007/s00010-013-0205-y

Cite this article as:
Dhara, B. & Ali, S. Aequat. Math. (2013) 86: 65. doi:10.1007/s00010-013-0205-y

Abstract

Let R be a ring. A map \({F : R \rightarrow R}\) is called a multiplicative (generalized)-derivation if F(xy) = F(x)yxg(y) is fulfilled for all \({x, y \in R}\) where \({g : R \rightarrow R}\) is any map (not necessarily derivation). The main objective of the present paper is to study the following situations: (i) \({F(xy) \pm xy \in Z}\), (ii) \({F(xy) \pm yx \in Z}\), (iii) \({F(x)F(y) \pm xy \in Z}\) and (iv) \({F(x)F(y) \pm yx \in Z}\) for all x, y in some appropriate subset of R. Moreover, some examples are also given.

Mathematics Subject Classification (2000)

16N6016U8016W25

Keywords

Prime ringsemiprime ringleft idealderivationmultiplicative derivationgeneralized derivationmultiplicative (generalized)-derivation

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsBelda College, BeldaPaschim MedinipurIndia
  2. 2.Department of MathematicsAligarh Muslim UniversityAligarhIndia