# MathSciDoc: An Archive for Mathematician ∫

#### Rings and Algebrasmathscidoc:1701.31002

Arkiv for Matematik, 1-18, 2015.12
Starting with a commutative ring $R$ and an ideal $I$ , it is possible to define a family of rings $R(I)_{a,b}$ , with $a,b \in R$ , as quotients of the Rees algebra $\oplus_{n \geq0} I^{n}t^{n}$ ; among the rings appearing in this family we find Nagata’s idealization and amalgamated duplication. Many properties of these rings depend only on $R$ and $I$ and not on $a$ , $b$ ; in this paper we show that the Gorenstein and the almost Gorenstein properties are independent of $a$ , $b$ . More precisely, we characterize when the rings in the family are Gorenstein, complete intersection, or almost Gorenstein and we find a formula for the type.
@inproceedings{v.2015families,
title={Families of Gorenstein and almost Gorenstein rings},
author={V. Barucci, M. D’Anna, and F. Strazzanti},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407854149824},
booktitle={Arkiv for Matematik},
pages={1-18},
year={2015},
}

V. Barucci, M. D’Anna, and F. Strazzanti. Families of Gorenstein and almost Gorenstein rings. 2015. In Arkiv for Matematik. pp.1-18. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407854149824.