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arXiv · 1512.07179

Families of Gorenstein and almost Gorenstein rings

Valentina Barucci·Marco D'Anna·Francesco Strazzanti
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Abstract

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 $\oplus_{n \geq 0} I^nt^n$; 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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Valentina Barucci, Marco D'Anna, Francesco Strazzanti. 2015-12-22. Families of Gorenstein and almost Gorenstein rings. https://doi.org/10.1007/s11512-016-0235-5

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