scholarly journals Uniform annihilators of systems of parameters

2021 ◽  
Author(s):  
Pham Quy
Keyword(s):  
Systems Of Parameters

scholarly journals A characterization of systems of parameters

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

scholarly journals An Algorithm to Calculate Optimal Homogeneous Systems of Parameters

1999 ◽  
Vol 27 (2) ◽  
pp. 171-184 ◽  
Author(s):  
G. Kemper
Keyword(s):  
Homogeneous Systems ◽  
Systems Of Parameters

scholarly journals On the length of the powers of systems of parameters in local ring

1990 ◽  
Vol 120 ◽  
pp. 77-88 ◽  
Author(s):  
Nguyen Tu Cuong
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Noetherian Ring ◽  
Finitely Generated ◽  
Systems Of Parameters ◽  
System Of Parameters ◽  
The Ideal

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.

Homogeneous systems of parameters in cohomology algebras of finite groups

2004 ◽  
Vol 82 (2) ◽  
pp. 110-121
Author(s):  
Tetsuro Okuyama ◽  
Hiroki Sasaki
Keyword(s):  
Finite Groups ◽  
Homogeneous Systems ◽  
Systems Of Parameters

Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings

1976 ◽  
Vol 43 (3) ◽  
pp. 511-531 ◽  
Author(s):  
Richard P. Stanley
Keyword(s):  
Magic Squares ◽  
Systems Of Parameters

scholarly journals Mora’s holy graal: Algorithms for computing in localizations at prime ideals

2015 ◽  
Vol 25 (07) ◽  
pp. 1125-1143 ◽  
Author(s):  
Magdaleen S. Marais ◽  
Yue Ren
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Computational Approach ◽  
Prime Ideals ◽  
Graded Algebra ◽  
Coordinate Ring ◽  
Localization Formula ◽  
Hilbert Polynomials ◽  
Systems Of Parameters ◽  
Appl Math

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.

scholarly journals On the Relation Type of Systems of Parameters

1995 ◽  
Vol 175 (1) ◽  
pp. 339-358 ◽  
Author(s):  
Y.H. Lai
Keyword(s):  
Relation Type ◽  
Systems Of Parameters

scholarly journals On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings

1992 ◽  
Vol 125 ◽  
pp. 105-114 ◽  
Author(s):  
Nguyen Tu Cuong
Keyword(s):  
Maximal Ideal ◽  
Noetherian Ring ◽  
Local Rings ◽  
Finitely Generated ◽  
Parameter Ideal ◽  
Systems Of Parameters ◽  
The Difference

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.

scholarly journals Hilbert polynomials of j-transforms

2016 ◽  
Vol 161 (2) ◽  
pp. 305-337
Author(s):  
SHIRO GOTO ◽  
JOOYOUN HONG ◽  
WOLMER V. VASCONCELOS
Keyword(s):  
Hilbert Functions ◽  
Local Rings ◽  
Hilbert Polynomials ◽  
Graded Module ◽  
Systems Of Parameters ◽  
Partial Systems

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.

Sign in / Sign up

Export Citation Format

Share Document