Semisimplicity and separability for pseudocompact algebras

Abstract

We give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such algebras analogous to those for finite dimensional algebras. We give a self-contained proof of the Wedderburn–Malcev Theorem for pseudocompact algebras.