Chain Conditions on Noetherian Rings by Prof. Susan Loepp

Wednesday, June 21 at 1:00pm to 1:45pm

Bronfman Science Center, 106

Mathematics Colloquium

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.  We give a brief history of catenary Noetherian rings and end with a surprising example.

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Mathematics & Statistics

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