Hilbert functions, analytic spread, and Koszul homology

1994 ◽  
pp. 401-422 ◽  
Author(s):  
Wolmer V. Vasconcelos
Keyword(s):  
Hilbert Functions ◽  
Analytic Spread ◽  
Koszul Homology

On equimultiplicity

1982 ◽  
Vol 91 (2) ◽  
pp. 207-213 ◽  
Author(s):  
M. Herrmann ◽  
U. Orbanz
Keyword(s):  
Prime Ideal ◽  
Local Ring ◽  
Analytic Spread

This note consists of some investigations about the condition ht(A) = l(A) where A is an ideal in a local ring and l(A) is the analytic spread of A (9).In (4) we proved the following: If R is a local ring and P a prime ideal such that R/P is regular then (under some technical assumptions) ht(P) = l(P) is equivalent to the equimultiplicity e(R) = e(RP). Also for a general ideal A (which need not be prime), the condition ht(A) = l(A) can be translated into an equality of certain multiplicities (see Theorem 0).

Hilbert functions and the extension functor

1989 ◽  
Vol 105 (3) ◽  
pp. 441-446 ◽  
Author(s):  
David Kirby
Keyword(s):  
Commutative Ring ◽  
Hilbert Functions ◽  
Definition Of

Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).

scholarly journals Interval conjectures for level Hilbert functions

2009 ◽  
Vol 321 (10) ◽  
pp. 2705-2715 ◽  
Author(s):  
Fabrizio Zanello
Keyword(s):  
Hilbert Functions

Gröbner bases specialization through Hilbert functions

2000 ◽  
Vol 34 (1) ◽  
pp. 1-8 ◽  
Author(s):  
M.-J. Gonzalez-Lopez ◽  
L. Gonzalez-Vega ◽  
C. Traverso ◽  
A. Zanoni
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Hilbert Functions
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