Families of Gorenstein and almost Gorenstein rings

Starting with a commutative ring R and an ideal I,it is possible to define a family of rings, as quotients of the Rees algebra; among the rings appearing inthis family we find Nagata's idealization and amalgamatedduplication. Many properties of these rings depend only on R and I; in this paper we show that this happens for the Gorenstein and the almost Gorenstein properties.More precisely, we characterize when the rings in the family are Gorenstein, complete intersection, or almost Gorenstein and wefind a formula for the type.