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International Journal of Mathematics and Mathematical Sciences - Volume 2004 2004, Issue 37, Pages 1957-1964



Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 8 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let R be a ring and S a nonempty subset of R. Suppose that θ and ϕ are endomorphisms of R. An additive mapping δ:R→R is called a left θ,ϕ-derivation resp., Jordan left θ,ϕ-derivation on S if δxy=θxδy+ϕyδx resp., δx2=θxδx+ϕxδx holds for all x,y∈S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is shown that if θ is an automorphism of R such that δx2=2θxδx holds for all x∈J, then either J⫅ZR or δJ=0. Further, a study of left θ,θ-derivations of a prime ring R has been made which acts either as a homomorphism or as an antihomomorphism of the ring R.





Autor: S. M. A. Zaidi, Mohammad Ashraf, and Shakir Ali

Fuente: https://www.hindawi.com/



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