On the generalized derivations of bimodules

Abstract

Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.

Keywords

Generalized derivation / separable algebra extension

References

[1] Brěsar M. On the distance of the composition of two derivations to the generalized derivations. Glasg Math J, 1991, 33: 89–93

[2] Elliger S. ¨Uber Automorphismen und Derivationen von Ringen. J Reine Angew Math, 1975, 277: 155–177

[3] Komatsu H. Generalized derivations of bimodules. Int J Pure Appl Math, 2012, 77: 579–593

[4] Miyashita Y. Finite outer Galois theory of non-commutative rings. J Fac Sci Hokkaido Univ Ser I, 1966, 19: 114–134

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg