dc.contributor.advisor Albrecht, Ulrich dc.contributor.author James, Daniel dc.date.accessioned 2017-04-21T15:15:33Z dc.date.available 2017-04-21T15:15:33Z dc.date.issued 2017-04-21 dc.identifier.uri http://hdl.handle.net/10415/5678 dc.description.abstract We 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.rights EMBARGO_GLOBAL en_US dc.subject Mathematics and Statistics en_US dc.title Dedekind Domains and the P-rank of Ext en_US dc.type PhD Dissertation en_US dc.embargo.length MONTHS_WITHHELD:6 en_US dc.embargo.status EMBARGOED en_US dc.embargo.enddate 2017-10-18 en_US
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