Properties of rings and of ring extensions that are invariant under group action

dc.contributor.advisor	Shapiro, Jay A.
dc.contributor.author	Schmidt, Amy Dannielle
dc.creator	Schmidt, Amy Dannielle
dc.date.accessioned	2015-07-29T18:35:17Z
dc.date.available	2015-07-29T18:35:17Z
dc.date.issued	2015
dc.description.abstract	We expand the work in invariant theory inspired by Hilbert's Fourteenth Problem. Given a commutative ring with identity $R$ and a subgroup $G$ of the automorphism group of $R$, the \textit{fixed ring} is $R^G:=\{r\in R\,\|\,\sigma(r)=r\;\text{for all}\;\sigma\in G\}$. That is, $R^G$ is the collection of elements of $R$ that are fixed by all automorphisms in $G$. Properties of $R$ inherited by $R^G$ and properties of the extension $R^G\subseteq R$ have been studied extensively. We call properties of $R$ that are inherited by $R^G$ \textit{invariant (under the group action by $G$)}.
dc.format.extent	50 pages
dc.identifier.uri	https://hdl.handle.net/1920/9627
dc.language.iso	en
dc.rights	Copyright 2015 Amy Dannielle Schmidt
dc.subject	Mathematics
dc.subject	Fixed ring
dc.subject	Group action
dc.subject	Invariant
dc.subject	Minimal ring extension
dc.title	Properties of rings and of ring extensions that are invariant under group action
dc.type	Dissertation
thesis.degree.discipline	Mathematics
thesis.degree.grantor	George Mason University
thesis.degree.level	Doctoral

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