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# 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.identifier.uri https://hdl.handle.net/1920/9627 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.language.iso en dc.rights Copyright 2015 Amy Dannielle Schmidt dc.subject Mathematics en_US dc.subject fixed ring en_US dc.subject group action en_US dc.subject invariant en_US dc.subject minimal ring extension en_US dc.title Properties of rings and of ring extensions that are invariant under group action dc.type Dissertation en thesis.degree.level Doctoral en thesis.degree.discipline Mathematics en thesis.degree.grantor George Mason University en
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