FINITE AUTOMORPHISM GROUPS OF REDUCED COMMUTATIVE RINGS

Abstract

Definitions of normality and separability for unitary commutative ring extensions are given from the perspective of algebraic and transcendental ring extensions. Necessary and sufficient conditions are given for the set of subrings T _i , R ⊆ T _i ⊆ S, in a normal separable extension S: R in which the extensions S: T _i are normal separable extensions, to map uniquely bijectively on the set of all subgroups of the Galois group of S: R.