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dc.contributor.advisorAlbrecht, Ulrich
dc.contributor.authorJames, Daniel
dc.date.accessioned2017-04-21T15:15:33Z
dc.date.available2017-04-21T15:15:33Z
dc.date.issued2017-04-21
dc.identifier.urihttp://hdl.handle.net/10415/5678
dc.description.abstractWe address what can be said of torsion-free finite rank modules $A$ and $B$ over a Dedekind domain $R$ when their Ext's are isomorphic, extending an answer to Fuchs' Problem 43 and its dual by Goeters. We obtain a result for the covariant case when $\hat{R_P}$ has infinite rank over $R$, noting that $A$ and $B$ are quasi-isomorphic iff the $P$-rank of their Hom sets match. In the contravariant case, we see $A$ and $B$ are quasi-isomorphic implies their extension groups are isomorphic, with the converse holding when again $\hat{R_P}$ has infinite rank over $R$. Along the way, we find equivalent conditions that hold for Noetherian domains whose completions are not complete in the $P$-adic topology.en_US
dc.rightsEMBARGO_GLOBALen_US
dc.subjectMathematics and Statisticsen_US
dc.titleDedekind Domains and the P-rank of Exten_US
dc.typePhD Dissertationen_US
dc.embargo.lengthMONTHS_WITHHELD:6en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2017-10-18en_US


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