Nearly Gorenstein semigroup rings

Among the Cohen-Macaulay rings, Gorenstein rings have a prominent role in many respects. Looking for other rings with similar properties, many authors have proposed several generalizations, and one of the most studied in the last years is the notion of nearly Gorenstein ring. In this talk, after an introduction to these rings, I will focus on some nearly Gorenstein semigroup rings. In particular, I will explain a characterization using the properties of the associated semigroup and I will give some results about their Cohen-Macaulay type. This is based on joint works with Alessio Moscariello, Raheleh Jafari and Santiago Zarzuela Armengou.