Families of Gorenstein and almost Gorenstein rings

V. Barucci Dipartimento di Matematica, Sapienza - Università di Roma M. D’Anna Dipartimento di Matematica e Informatica, Università degli Studi di Catania F. Strazzanti Dipartimento di Matematica, Università di Pisa

Rings and Algebras mathscidoc: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.
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  title={Families of Gorenstein and almost Gorenstein rings},
  author={V. Barucci, M. D’Anna, and F. Strazzanti},
  booktitle={Arkiv for Matematik},
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.
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