Dumitru Stamate
University of Bucharest, Bucharest, Romania

The trace of a module $M$ is the sum of the images of all $R$-module homomorphisms from $R$ into $M$. When $R$ has a canonical module $\omega_R$, the trace of the latter is called the canonical trace ideal of $R$ and it measures how far is the ring from being Gorenstein. I will report on the use of the canonical trace to define new classes of rings sitting between the Cohen-Macaulay and the Gorenstein ones. This is based on joint works with Herzog and Hibi, and with Herzog and Kumashiro, respectively.