We study some properties of a family of rings that are obtained as quotients of the Rees algebra associated with a ring R and an ideal I. 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 these rings are integral domains, reduced, quasi-Gorenstein, or satisfy Serre's conditions.

NEW ALGEBRAIC PROPERTIES OF QUADRATIC QUOTIENTS OF THE REES ALGEBRA

Marco D'Anna
;
2019

Abstract

We study some properties of a family of rings that are obtained as quotients of the Rees algebra associated with a ring R and an ideal I. 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 these rings are integral domains, reduced, quasi-Gorenstein, or satisfy Serre's conditions.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/319860
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