Generalized skew derivations characterized by acting on zero products.
The goal of this paper is to generalize the result from the recent paper by \textit{M. A. Chebotar}, \textit{W.-F. Ke} and \textit{P.-H. Lee} [Pac. J. Math. 216, No. 2, 217-228 (2004; see the review Zbl 1078.16034 above)] characterizing derivations by their actions on zero products to generalized skew derivations. The following situation is considered: \(A\) is a prime ring whose symmetric Martindale ring of quotients contains a nontrivial idempotent, \(\sigma\) is an automorphism of \(A\), and \(g,\delta\colon A\to A\) are additive maps such that \(xy=0\) implies \(\sigma(x)d(y)+\delta(x)y=0\). Then \(g\) and \(\delta\) are described as certain generalized \(\sigma\)-derivations on a nonzero ideal of \(A\).
scientific article; zbMATH DE number 2138446