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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