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Families of Gorenstein and almost Gorenstein rings
Arkiv för Matematik ( IF 0.7 ) Pub Date : 2016-07-27 , DOI: 10.1007/s11512-016-0235-5
V. Barucci , M. D’Anna , F. Strazzanti

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.

中文翻译:

Gorenstein和几乎Gorenstein戒指的家庭

从交换环\(R \)和理想\(I \)开始,可以定义一系列环\(R(I)_ {a,b} \)和\(a,b \在R \中),作为里斯代数\(\ oplus_ {n \ geq0} I ^ {n} t ^ {n} \)的商;在这个家族出现的戒指中,我们发现了永田的理想化和合并的重复。这些环的许多属性仅取决于\(R \)和\(I \),而不取决于\(a \),\(b \);在本文中,我们证明了Gorenstein和几乎Gorenstein属性与\(a \),\(b \)独立。更准确地说,我们描述族中的环何时是Gorenstein,完全交点或几乎是Gorenstein,并找到该类型的公式。
更新日期:2016-07-27
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