Chain Conditions on Noetherian Integral Domains and Noetherian Unique Factorization Domains by Prof. Susan Loepp

Friday, September 15 at 1:00pm to 1:45pm

Stetson Court classroom, 101 Stetson Court, Williamstown, MA, 01267

Mathematics Faculty Seminar

Abstract:  Noetherian rings are known to satisfy some nice chain conditions.  Indeed, they are defined to satisfy the famous ascending chain condition.  In this talk, we will consider another relatively simple chain condition.

Let P and Q be prime ideals of a Noetherian ring R such that P is contained in Q and such that two saturated chains of prime ideals starting at P and ending at Q have the same length.  If this property holds for all such pairs P and Q, then R is said to be catenary.

In this talk, we give a brief history of catenary Noetherian integral domains, and then present new results about catenary and noncatenary integral domains.  In particular, we present a new result on how noncatenary a Noetherian unique factorization domain can be.  The results presented in this talk were proved by the 2017 SMALL commutative algebra group, including Tim Kostolansky ‘18 and Alex Semendinger ’18.

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Mathematics & Statistics

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