We study some properties of a family of rings R(I)_{a,b} that are obtained as quotients of the Rees algebra associated with a ring R and an ideal I. In particular, we give a complete description of the spectrum of every member of the family and describe the localizations at a prime ideal. Consequently, we are able to characterize the Cohen–Macaulay and Gorenstein properties, generalizing known results stated in the local case. Moreover, we study when R(I)_{a,b} is an integral domain, reduced, quasi-Gorenstein, or satisfies Serre’s conditions.

New algebraic properties of quadratic quotients of the Rees algebra

Strazzanti F
2019-01-01

Abstract

We study some properties of a family of rings R(I)_{a,b} that are obtained as quotients of the Rees algebra associated with a ring R and an ideal I. In particular, we give a complete description of the spectrum of every member of the family and describe the localizations at a prime ideal. Consequently, we are able to characterize the Cohen–Macaulay and Gorenstein properties, generalizing known results stated in the local case. Moreover, we study when R(I)_{a,b} is an integral domain, reduced, quasi-Gorenstein, or satisfies Serre’s conditions.
2019
18
3
N/A
N/A
https://www.worldscientific.com/doi/abs/10.1142/S0219498819500476
https://arxiv.org/pdf/1706.06180.pdf
Idealization; amalgamated duplication; quasi-Gorenstein rings; localizations; Serre’s conditions.
D'Anna M; Strazzanti F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1789071
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