Fri, September 27, 2019
4:45 pm - 5:45 pm
Cockins Hall 240
Title: Lower-Finite Modules Over Commutative Rings
Speaker: Luke Everett Harmon, University of Colorado - Colorado Springs
Abstract: A partially ordered set (P,<) is lower-finite provided P is infinite and for each x in P, there are but finitely many elements y in P such that y<x. We will call a module M lower-finite if the set of proper submodules of M, partially ordered by set-theoretic containment, is lower-finite. We will introduce the (well-studied) class of Jonsson modules and use them to classify the infinitely generated, lower-finite modules over a commutative ring. In conclusion, we will discuss the progress we have made in classifying the finitely generated, lower-finite modules over a commutative ring.