Baer's extension equivalence

Abstract

We revisit Reinhold Baer's work on equivalent extensions, which can be considered as a forerunner of the authors' series of equivalence theorems. Our focus is on a paper entitled Extension Types of Abelian Groups published by Baer in 1949. In this paper, the main results were for a rather restrictive class of extensions called little extensions, but the notion of two extensions of A by B being equivalent given there are generally applicable. Our theme here is that Baer's vision and understanding of extensions placed him much ahead of the time in which he studied the subject in the 1930's and '40's.