hilbert coefficients
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2021 ◽  
Author(s):  
Kazuho Ozeki ◽  
Hoang Truong ◽  
Yen Hoang
Keyword(s):  

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Cao Huy Linh ◽  
Ton That Quoc Tan
Keyword(s):  

Author(s):  
Kumari Saloni

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.


2019 ◽  
Vol 30 (02) ◽  
pp. 379-396
Author(s):  
V. H. Jorge Pérez ◽  
T. H. Freitas

Let [Formula: see text] be a commutative quasi-local ring (with identity [Formula: see text]), and let [Formula: see text] be an [Formula: see text]-ideal such that [Formula: see text]. For [Formula: see text] an Artinian [Formula: see text]-module of N-dimension [Formula: see text], we introduce the notion of Hilbert-coefficients of [Formula: see text] relative to [Formula: see text] and give several properties. When [Formula: see text] is a co-Cohen–Macaulay [Formula: see text]-module, we establish the Northcott’s inequality for Artinian modules. As applications, we show some formulas involving the Hilbert coefficients and we investigate the behavior of these multiplicities when the module is the local cohomology module.


2019 ◽  
Vol 18 (10) ◽  
pp. 1950191 ◽  
Author(s):  
Le Xuan Dung ◽  
Le Tuan Hoa

New upper and lower bounds on the Castelnuovo–Mumford regularity are given in terms of the Hilbert coefficients. Examples are provided to show that these bounds are in some sense nearly sharp.


2019 ◽  
Vol 11 (4) ◽  
pp. 573-604
Author(s):  
Shreedevi K. Masuti ◽  
Kumari Saloni
Keyword(s):  

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