PROPERTIES OF RING EXTENSIONS INVARIANT UNDER GROUP ACTION

Abstract

Let G be a subgroup of the automorphism group of a commutative ring with identity T. Let R be a subring of T. We show that RG ⊂ T G is a minimal ring extension whenever R ⊂ T is a minimal extension under various assumptions. Of the two types of minimal ring extensions, integral and integrally closed, both of these properties are passed from R ⊂ T to RG ⊆ T G. An integrally closed minimal ring extension is a flat epimorphic extension as well as a normal pair. We show that each of these properties also pass from R ⊂ T to RG ⊆ T G under certain group action.