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Additive maps having a generalized derivation expansion

Tsiu-Kwen Lee

Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Member of Mathematics Division, NCTS (Taipei Office).

https://doi.org/10.1142/S0219498815500486Cited by:7 (Source: Crossref)

Abstract

Let R be a prime ring with extended centroid C. We prove that an additive map from R into RC + C can be characterized in terms of left and right b-generalized derivations if it has a generalized derivation expansion. As a consequence, a generalization of the Noether–Skolem theorem is proved among other things: A linear map from a finite-dimensional central simple algebra into itself is an elementary operator if it has a generalized derivation expansion.

Keywords:

AMSC: 16N60, 16R60, 16W25, 16W10

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