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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