Additive mapping acting as generalized (mu; nu)-derivation on semi-prime rings

Muzibur Rahman Mozumdr; Abu Zaid Ansari; Arshad Madni

doi:10.5269/bspm.68530

Muzibur Rahman Mozumdr Aligarh Muslim University
Abu Zaid Ansari Islamic University of Madinah
Arshad Madni Aligarh Muslim University

Abstract

The objective of this paper is to study the following: Let A be a (m+n 􀀀 1)!-torsion free semi-prime ring. Suppose that G; g : A ! A are two additive mappings satisfying the algebraic identity G(rm+n) = G(rm)(rn) + (rm)g(rn)
for all r 2 A: Then G will be a generalized (; )-derivation with associated (; )-derivation g on A. On the other hand, it is proved that G1 is a generalized left (; )-derivation associated with left (; )-derivation g1 on A if they satisfy the algebraic identity G1(rm+n) = (rn)G1(rm) + (rm)g1(rn) for all r 2 A. We will also examine criticism and provide example.

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