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∈R, as quotients of the Rees algebra ⊕n≥0Intn; 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.
Families of Gorenstein and Almost Gorenstein Rings / Barucci, Valentina; D'Anna, M.; Strazzanti, F.. - In: ARKIV FÖR MATEMATIK. - ISSN 0004-2080. - STAMPA. - 54:2(2016), pp. 321-338. [10.1007/s11512-016-0235-5]
Families of Gorenstein and Almost Gorenstein Rings
BARUCCI, Valentina;
2016
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∈R, as quotients of the Rees algebra ⊕n≥0Intn; 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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Barucci_Families-of-Gorenstein_2016.pdf
solo gestori archivio
Note: Articolo
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
1.19 MB
Formato
Adobe PDF
|
1.19 MB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
