systems of parameters
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Author(s):  
Katharine Shultis ◽  
Peder Thompson

A commutative noetherian local ring ( R , m ) (R,\mathfrak {m}) is Gorenstein if and only if every parameter ideal of R R is irreducible. Although irreducible parameter ideals may exist in non-Gorenstein rings, Marley, Rogers, and Sakurai show there exists an integer ℓ \ell (depending on R R ) such that R R is Gorenstein if and only if there exists an irreducible parameter ideal contained in m ℓ \mathfrak {m}^\ell . We give upper bounds for ℓ \ell that depend primarily on the existence of certain systems of parameters in low powers of the maximal ideal.



This paper restates the definition of the nice m-system of parameters for Artinian modules. It also shows its effects on the differences between lengths and multiplicities of certain systems of parameters for Artinian modules: In particular, if is a nice m-system of parameters then the function is a polynomial having very nice form. Moreover, we will prove some properties of the nice m-system of parameters for Artinian modules. Especially, its effect on the annihilation of local homology modules of Artinian module A.



2019 ◽  
Vol 13 (9) ◽  
pp. 2081-2102 ◽  
Author(s):  
Juliette Bruce ◽  
Daniel Erman


2018 ◽  
Vol 10 (1) ◽  
pp. 139-151
Author(s):  
Katharine Shultis


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.



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.



2015 ◽  
Vol 276 (2) ◽  
pp. 281-286
Author(s):  
Christine Berkesch Zamaere ◽  
Stephen Griffeth ◽  
Ezra Miller


2014 ◽  
Vol 4 (3(70)) ◽  
pp. 18
Author(s):  
Володимир Ігорович Романовський ◽  
Тетяна Миколаївна Загородня


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