Generalized Depth and Associated Primes in the Perfect Closure $R^\infty$

dc.contributor.advisor	Epstein, Neil
dc.contributor.author	Whelan, George
dc.creator	Whelan, George
dc.date.accessioned	2018-10-22T01:19:46Z
dc.date.available	2018-10-22T01:19:46Z
dc.date.issued	2017
dc.description.abstract	\indent Letting $(S, \mathfrak{n})$ be a Noetherian local ring, and $M$ be a finitely generated $S$-module, the notions of $\depth_S(M)$ and associated primes over $M$, denoted $\Ass_S(M)$, are fundamental concepts in commutative algebra. However, if $S$ is non-Noetherian, both of these notions become more subtle. Prime ideals in this scenario may then be categorized as associated primes, weakly associated primes, strong Krull primes, and Krull primes, respectively $\Ass_S(M)$, $\wAss_{S} (M)$, $\sK_S(M)$, and $\K_S(M)$. Likewise, any study of depth must distinguish between $\cdepth_S(M)$, $\kdepth_S(M)$, and $\rdepth_S(M)$.
dc.format.extent	67 pages
dc.identifier.uri	https://hdl.handle.net/1920/11239
dc.language.iso	en
dc.rights	Copyright 2017 George Whelan
dc.subject	Mathematics
dc.title	Generalized Depth and Associated Primes in the Perfect Closure $R^\infty$
dc.type	Dissertation
thesis.degree.discipline	Mathematics
thesis.degree.grantor	George Mason University
thesis.degree.level	Ph.D.

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