Ring extensions invariant under group action

2014/03/26 by Schmidt, Amy
#13A15 #13B202 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A50 #Secondary 13B21

paper · doi:10.48550/arxiv.1403.6733

Abstract

Let G be a subgroup of the automorphism group of a commutative ring with identity T. Let R be a subring of T such that R is invariant under the action by G. We show R^G⊂ 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 R^G⊂ T^G. An integrally closed minimal ring extension is a flat epimorphic extension as well as a normal pair. We show each of these properties also pass from R⊂ T to R^G⊆ T^G under certain group action.

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