Viet Dung Nguyen (Ohio University - Zanesville)


Title: The endo-structure of direct sums of indecomposable modules.


Abstract: A right module $M$ over an associative ring with identity is called endofinite if it has finite length as a left module over its endomorphism ring. It is well-known, due to W. Crawley-Boevey (1992), that every endofinite module $M$ is a direct sum of indecomposable modules $M_i$, and the number of isomorphism classes of $M_i$ is finite. Let $M = \oplus_{i\in I} M_i$ be an indecomposable decomposition of a module $M$, and let $S$ be the endomorphism ring of $M$. A natural question is to find (as weak as possible) conditions, in terms of the $S$-structure of $M$, which would ensure that there are only finitely many non-isomorphic members among the modules $M_i$. I will discuss several recent results in this direction, including recent work of B. Huisgen-Zimmermann and M. Saorin, and my related investigation on this topic.