scholarly journals On the Hilbert coefficients, depth of associated graded rings and reduction numbers

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Amir Mafi ◽  
Dler Naderi
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals Hilbert coefficients and Buchsbaumness of associated graded rings

2003 ◽  
Vol 181 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Shiro Goto ◽  
Koji Nishida
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals Hilbert Coefficients and the Depths of Associated Graded Rings

1997 ◽  
Vol 56 (1) ◽  
pp. 64-76 ◽  
Author(s):  
Sam Huckaba ◽  
Thomas Marley
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals The structure of sally modules and Buchsbaumness of associated graded rings

2013 ◽  
Vol 212 ◽  
pp. 97-138 ◽  
Author(s):  
Kazuho Ozeki
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Primary Ideal ◽  
Graded Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Noetherian Local Ring ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

AbstractLet A be a Noetherian local ring with the maximal ideal m, and let I be an m-primary ideal in A. This paper examines the equality on Hilbert coefficients of I first presented by Elias and Valla, but without assuming that A is a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring of I.

scholarly journals Hilbert coefficients and the associated graded rings

1999 ◽  
Vol 128 (4) ◽  
pp. 963-973 ◽  
Author(s):  
Hsin-Ju Wang
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals The structure of sally modules and Buchsbaumness of associated graded rings

2013 ◽  
Vol 212 ◽  
pp. 97-138 ◽  
Author(s):  
Kazuho Ozeki
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Primary Ideal ◽  
Graded Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Noetherian Local Ring ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

AbstractLetAbe a Noetherian local ring with the maximal ideal m, and letIbe an m-primary ideal inA. This paper examines the equality on Hilbert coefficients ofIfirst presented by Elias and Valla, but without assuming thatAis a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring ofI.

scholarly journals Buchsbaumness of the associated graded rings of filtration

2020 ◽  
pp. 2250039
Author(s):  
Kumari Saloni
Keyword(s):  
Local Ring ◽  
Alternative Proof ◽  
Sufficient Condition ◽  
Graded Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Dimension Formula ◽  
Hilbert Coefficients ◽  
Associated Graded Rings ◽  
Good Filtration

Let [Formula: see text] be a Noetherian local ring of dimension [Formula: see text] and [Formula: see text] an [Formula: see text]-primary ideal of [Formula: see text]. In this paper, we discuss a sufficient condition, for the Buchsbaumness of the local ring [Formula: see text] to be passed onto the associated graded ring of filtration. Let [Formula: see text] denote an [Formula: see text]-good filtration. We prove that if [Formula: see text] is Buchsbaum and the [Formula: see text] -invariant, [Formula: see text] and [Formula: see text], coincide then the associated graded ring [Formula: see text] is Buchsbaum. As an application of our result, we indicate an alternative proof of a conjecture, of Corso on certain boundary conditions for Hilbert coefficients.

Hilbert Coefficients and the Depth of Associated Graded Rings with Respect to Parameter Ideals

2019 ◽  
Vol 47 (2) ◽  
pp. 431-442
Author(s):  
Cao Huy Linh ◽  
Van Duc Trung
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals Depth of associated graded rings via Hilbert coefficients of ideals

2005 ◽  
Vol 201 (1-3) ◽  
pp. 126-141 ◽  
Author(s):  
Alberto Corso ◽  
Claudia Polini ◽  
Maria Evelina Rossi
Keyword(s):  
Graded Rings ◽  
Hilbert Coefficients ◽  
Associated Graded Rings

scholarly journals Associated graded rings of one-dimensional analytically irreducible rings

2006 ◽  
Vol 304 (1) ◽  
pp. 349-358 ◽  
Author(s):  
V. Barucci ◽  
R. Fröberg
Keyword(s):  
Graded Rings ◽  
One Dimensional ◽  
Associated Graded Rings
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