# Marco D'Anna: Almost Gorenstein rings and further generalizations: the one-dimensional case

**Time: **
Wed 2023-03-01 13.15

**Location: **
Albano, Cramér room

**Participating: **
Marco D'Anna, Catania

**Abstract**

I will first present the class of almost Gorenstein rings, focusing on the one-dimensional case. This notion was introduced by Barucci and Froberg for algebroid curves and it has been recently generalized (by Goto and others) and widely studied for more general one-dimensional rings and, successively, in any dimension.

In the one-dimensional case, other possible generalizations of Gorenstein and almost Gorenstein has been proposed; these classes are close to Gorenstein and almost Gorenstein rings under different aspects. I will describe one of these new classes, whose definition is motivated by the relationships between the properties of a local one-dimensional ring \((R,\mathfrak{m})\) and those of the *R*-algebra \(\mathfrak{m}:\mathfrak{m}\).