This chapter introduces a class of algebras that enjoys some of the attractive properties of semisimple algebras. These are the separable algebras. For F-algebras, separability is more restrictive than semisimplicity. One purpose of this chapter is to give an effective characterization of separable algebras over fields. In the course of obtaining this characterization, we will establish some properties of separable algebras that are important even when they are applied only to semisimple algebras.
KeywordsCommutative Ring Surjective Homomorphism Separable Extension Finite Representation Type Finite Field Extension
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