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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1110268
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 8
social impact