Integral closure and bounds for quotients of multiplicities of monomial ideals
type: Item
instance of: scholarly article
title: Integral closure and bounds for quotients of multiplicities of monomial ideals
zbMATH Open document ID: 1388.13050
author: Carles Bivià-Ausina
published in: Journal of Algebra
publication date: 2018-03-01T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/103293
review text: The author studies the multiplicity (and related notions) of ideals in the ring \(\mathcal{O}_{n}\) of complex analytic function germs \(f:(\mathbb{C} ^{n},0)\rightarrow \mathbb{C}\). In particular: monomial ideals, mixed multiplicities (for systems of ideals), Newton filtration of \(\mathcal{O}_{n} \) and integral closure of ideals. According to the author the main result is: for a given pair of monomials ideals \(I\) and \(J\) of finite colength in \( \mathcal{O}_{n}\) some power of \(I\) admits a reduction formed by homogeneous polynomials with respect to the Newton filtration induced by \(J\) if and only if the quotient of multiplicities \(e(I)/e(J)\) attains a suitable upper bound expressed in terms of the Newton polyhedra of \(I\) and \(J\).
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 13B22
zbMATH DE Number: 6845990
zbMATH Keywords: multiplicity
zbMATH Keywords: integral closure
zbMATH Keywords: mixed multiplicity
zbMATH Keywords: monomial ideal
zbMATH Keywords: Newton polyhedra
zbMATH Keywords: Newton filtration
MaRDI profile type: Publication
OpenAlex ID: W2790139170
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DOI: 10.1016/J.JALGEBRA.2017.12.030
description: scientific article; zbMATH DE number 6845990