Speaker: Cosmin Roman, The Ohio State University-Lima

Title: On direct sums of Baer modules

Abstract: The recently introduced concept of Baer modules has strong connections to the well-known extending or CS modules (for example, every nonsingular extending module is Baer). Recall that a module M is called Baer, if every left ideal I of the endomorphism ring of M which annihilates an arbitrary subset (or submodule) of M, is generated by an idempotent. Similar to the extending module case, it is well-known that direct sums of Baer modules are not always Baer. The investigations on when direct sums of Baer modules are Baer are of interest as these can have useful implications for direct sums of nonsingular extending modules in addition to the natural interest in this question in its own right.

In this talk I will present results on when is a free module Baer, as well as when is an arbitrary direct sum of copies of a module M, Baer? As a consequence, among other results we obtain necessary and sufficient conditions for when is a free nonsingular module, extending. Examples will be presented to illustrate the results.