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Uncountable Excellent Rings With Countably Many Prime Ideals by Anya Michaelsen '19

Mon, May 6th, 2019
1:00 pm
- 1:45 pm

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Uncountable Excellent Rings With Countably Many Prime Ideals by Anya Michaelsen ’19, Mathematics Senior Thesis Defense, Monday, May 6, 1 — 1:45 pm, Stetson Court Classroom 101

Abstract:  It was unknown until 2016 that a (nontrivial) example of an uncountable Noetherian ring with only countably many prime ideals exists. The first example of such a ring, constructed by C. Colbert, has many desirable properties such as every ideal is generated by polynomials. However, it was unknown if it had other nice structural properties, like excellent or regular local (to be defined). In this talk, we will show by construction the existence of many (nontrivial) uncountable, excellent, regular local rings that have only countably many prime ideals. As a consequence, these rings are also UFDs and Noetherian, extending Colbert’s result.

 

 

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