Generalized skew derivations characterized by acting on zero products

Tsiu-Kwen Lee

Vol. 216 (2004), No. 2, 293–301

DOI: 10.2140/pjm.2004.216.293

Abstract

Let A be a prime ring whose symmetric Martindale quotient ring contains a nontrivial idempotent. Generalized skew derivations of A are characterized by acting on zero products. Precisely, if g,δ: A → A are additive maps such that σ(x)g(y) + δ(x)y = 0 for all x,y ∈ A with xy = 0, where σ is an automorphism of A, then both g and δ are characterized as specific generalized σ-derivations on a nonzero ideal of A.

Milestones

Received: 19 June 2003

Revised: 21 August 2003

Published: 1 October 2004