Marco D'Anna: Almost Gorenstein rings and further generalizations: the one-dimensional case
Tid: On 2023-03-01 kl 13.15
Plats: Albano, Cramér room
Medverkande: 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 \(\mathfrak{m}:\mathfrak{m}\).