Haydee Lindo

Harvey Mudd College

Trace Ideals in Commutative Algebra

The well know trace map on matrices can be generalized to a map on any module over a commutative ring.  The image of such a map is a trace ideal. In particular, given a ring R, the trace ideal of an R-module M is the ideal generated by the homomorphic images of M in R, and this construction has recently garnered new attention within commutative algebra.  In this talk we will outline some recent developments in the theory of trace ideals, with some applications to endomorphism rings, rigid modules, and classifications of commutative rings.