Some types of Separable Extensions of Rings

Abstract

In [5] we defined the notion of separable extensions of a ring as a generalization of that of separable algebras. In this paper we try to introduce the notion of ‘central’ separable algebras to separable extensions. Such extensions are viewed in §2. But we do not know that it is suitable or not to call them central separable extensions. As the Morita theorem for projective generators is fundamental to examine the central separable algebras we generalize it in §1. Let R be a ring and let A and B be left R-modules. We assume that R-module B is isomorphic to a direct summand of a finite direct sum of copies isomorphic to A.