PROPERTIES OF RING EXTENSIONS INVARIANT UNDER GROUP ACTION | Zendy

Amy Dannielle Schmidt | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

PROPERTIES OF RING EXTENSIONS INVARIANT UNDER GROUP ACTION

Author(s) -

Amy Dannielle Schmidt

Publication year - 2017

Publication title -

international electronic journal of algebra

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.268

H-Index - 5

ISSN - 1306-6048

DOI - 10.24330/ieja.295752

Subject(s) - subring , integrally closed , mathematics , automorphism , ring (chemistry) , extension (predicate logic) , commutative ring , invariant (physics) , combinatorics , group ring , pure mathematics , group (periodic table) , discrete mathematics , commutative property , physics , computer science , mathematical physics , chemistry , organic chemistry , quantum mechanics , mechanical engineering , engineering , programming language

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research