One-dimensional local rings with reduced associated graded ring and their Hilbert functions

1980 ◽  
Vol 32 (3-4) ◽  
pp. 391-405 ◽  
Author(s):  
Ferruccio Orecchia
Keyword(s):  
Hilbert Functions ◽  
Local Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
One Dimensional

On the Buchsbaumness of the Associated Graded Ring of a One-Dimensional Local Ring

2009 ◽  
Vol 37 (5) ◽  
pp. 1594-1603 ◽  
Author(s):  
M. D'Anna ◽  
M. Mezzasalma ◽  
V. Micale
Keyword(s):  
Local Ring ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
One Dimensional

On the length formula of Hoskin and Deligne and associated graded rings of two-dimensional regular local rings

1992 ◽  
Vol 111 (3) ◽  
pp. 423-432 ◽  
Author(s):  
Bernard L. Johnston ◽  
Jugal Verma
Keyword(s):  
Hilbert Series ◽  
Primary Ideal ◽  
Local Rings ◽  
Classical Theorem ◽  
Two Dimensional ◽  
Graded Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Associated Graded Rings ◽  
Image Position

Let (R, m) be a 2-dimensional regular local ring and I an m-primary ideal. The aim of this paper is to find conditions on I so that the associated graded ring of I,and the Rees ring of I,where t is an indeterminate, are Cohen–Macaulay (resp. Gorenstein). To this end, we use the results and techniques from Zariski's theory of complete ideals ([14], appendix 5) and its later generalizations and refinements due to Huneke [7] and Lipman[8]. The main result is an application of three deep theorems: (i) a generalization of Macaulay's classical theorem on Hilbert series of Gorenstein graded rings [13], (ii) a generalization of the Briançon–Skoda theorem due to Lipman and Sathaye [9], and (iii) a formula for the length of R/I, where I is a complete m-primary ideal, due to Hoskin[4] and Deligne[1].

NORMAL HILBERT FUNCTIONS OF ONE-DIMENSIONAL LOCAL RINGS

2001 ◽  
Vol 29 (1) ◽  
pp. 333-341
Author(s):  
Valentina Barucci ◽  
Marco D'Anna ◽  
Ralf Fröberg
Keyword(s):  
Hilbert Functions ◽  
Local Rings ◽  
One Dimensional
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