Completions of Catenary Domains by Andrew Aramini '19, Mathematics Senior Thesis Defense

Completions of Catenary Domains by Andrew Aramini ’19, Mathematics Senior Thesis Defense, Tuesday, May 14, 10:30 am, Stetson Court Classroom 105

Abstract:  Given a complete local ring T, how do we know if T is the completion of a catenary integral domain? The SMALL 2017 Commutative Algebra Group characterized the completions of noncatenary integral domains, but the problem of characterizing the completions of catenary integral domains is still open. In this talk, we make progress towards answering this open problem by showing there exists a domain S whose completion is T such that some desired prime ideals of T are “glued” together in S; that is, that each of those prime ideals have the same intersection with S.