Let (R, m) be a one-dimensional reduced (Noetherian) local ring with finite integral closure ((R) over bar, M-1,..., M-t). We assume further that R/m similar or equal to (R) over bar /M-i for each i and that Card(R/m) greater than or equal to t. We study for such a ring R the associated graded ring and the Hilbert series, with respect to the normal filtration of an m-primary ideal I, R superset of or equal to (I) over bar superset of or equal to (I-2) over bar superset of or equal to (...). We make use of the value semigroup of R and in particular of some results of (7).
Normal Hilbert functions of one-dimensional local rings / Barucci, Valentina; Marco, D'Anna; Ralf, Froberg. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 29:1(2001), pp. 333-341. [10.1081/agb-100000804]
Normal Hilbert functions of one-dimensional local rings
BARUCCI, Valentina;
2001
Abstract
Let (R, m) be a one-dimensional reduced (Noetherian) local ring with finite integral closure ((R) over bar, M-1,..., M-t). We assume further that R/m similar or equal to (R) over bar /M-i for each i and that Card(R/m) greater than or equal to t. We study for such a ring R the associated graded ring and the Hilbert series, with respect to the normal filtration of an m-primary ideal I, R superset of or equal to (I) over bar superset of or equal to (I-2) over bar superset of or equal to (...). We make use of the value semigroup of R and in particular of some results of (7).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
