PROPERTIES OF RING EXTENSIONS INVARIANT UNDER GROUP ACTION

Year 2017, Volume: 21 Issue: 21, 39 - 54, 17.01.2017

Amy Schmidt

https://doi.org/10.24330/ieja.295752

Cited By: 3

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. 

Keywords

Fixed ring, ring of invariants

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