scholarly journals Uniform annihilators of systems of parameters

2021 ◽  
Author(s):  
Pham Quy

1996 ◽  
Vol 124 (3) ◽  
pp. 671-675 ◽  
Author(s):  
Sankar P. Dutta ◽  
Paul C. Roberts




1990 ◽  
Vol 120 ◽  
pp. 77-88 ◽  
Author(s):  
Nguyen Tu Cuong

Throughout this note, A denotes a commutative local Noetherian ring with maximal ideal m and M a finitely generated A-module with dim (M) = d. Let x1, …, xd be a system of parameters (s.o.p. for short) for M and I the ideal of A generated by x1, …, xd.



2004 ◽  
Vol 82 (2) ◽  
pp. 110-121
Author(s):  
Tetsuro Okuyama ◽  
Hiroki Sasaki




2015 ◽  
Vol 25 (07) ◽  
pp. 1125-1143 ◽  
Author(s):  
Magdaleen S. Marais ◽  
Yue Ren

This paper discusses a computational treatment of the localization [Formula: see text] of an affine coordinate ring [Formula: see text] at a prime ideal [Formula: see text] and its associated graded algebra [Formula: see text] with the means of computer algebra. Building on Mora’s paper [T. Mora, La queste del Saint [Formula: see text]: A computational approach to local algebra, Discrete Appl. Math. 33 (1991) 161–190], we present shorter proofs on two of the central statements and expand on the applications touched by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of [Formula: see text]. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.



1995 ◽  
Vol 175 (1) ◽  
pp. 339-358 ◽  
Author(s):  
Y.H. Lai


1992 ◽  
Vol 125 ◽  
pp. 105-114 ◽  
Author(s):  
Nguyen Tu Cuong

Let A be a commutative local Noetherian ring with the maximal ideal m and M a finitely generated A-module, d = dim M. It is well-known that the difference between the length and the multiplicity of a parameter ideal q of Mgives a lot of informations on the structure of the module M. For instance, M is a Cohen-Macaulay (CM for short) module if and only if IM(q) = 0 for some parameter ideal q or M is Buchsbaum module (see [S-V]) if and only if IM(q) is a constant for all parameter ideals q of M.



2016 ◽  
Vol 161 (2) ◽  
pp. 305-337
Author(s):  
SHIRO GOTO ◽  
JOOYOUN HONG ◽  
WOLMER V. VASCONCELOS

AbstractWe study transformations of finite modules over Noetherian local rings that attach to a module M a graded module H(x)(M) defined via partial systems of parameters x of M. Despite the generality of the process, which are called j-transforms, in numerous cases they have interesting cohomological properties. We focus on deriving the Hilbert functions of j-transforms and studying the significance of the vanishing of some of its coefficients.



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