Sequences of linear type
type: Item
instance of: scholarly article
title: Sequences of linear type
zbMATH Open document ID: 0595.13001
DOI: 10.1016/0021-8693(85)90211-X
author: Douglas L. Costa
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let A be a commutative ring and I an ideal of A. I is called an ideal of linear type if the canonical surjection from the symmetric algebra of I to the Rees algebra of I is an isomorphism. A sequence \(a_ 1,..,a_ n\) of A is of linear type if each ideal \(I_ i=(a_ 1,...,a_ i)\), \(i=1,...,n\), is an ideal of linear type. It is shown that if \((I_ iI^ t:a_ i)\cap I^ t=I_{i-1}I^{t-1}\) for \(i=1,...,n\) and each integer \(t\geq 1\), then \(I=(a_ 1,...,a_ n)\) is an ideal of linear type. This yields Huneke's result that a d-sequence is a sequence of linear type. A characterization of sequences of linear type in the form of an induction theorem is given and this is used to derive a result on monomial sequences.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 3957255
zbMATH Keywords: ideal of linear type
zbMATH Keywords: symmetric algebra
zbMATH Keywords: Rees algebra
zbMATH Keywords: d-sequence
zbMATH Keywords: sequence of linear type
zbMATH Keywords: monomial sequences
reviewed by: D. D. Anderson
MaRDI profile type: Publication
cites work: Complete intersections and symmetric algebras
cites work: On the torsion-freeness of the symmetric powers of an ideal
cites work: On relative regular sequences
cites work: Approximation complexes of blowing-up rings
cites work: Q3964688
cites work: The theory of d-sequences and powers of ideals
cites work: On the symmetric and Rees algebra of an ideal generated by a d-sequence
cites work: On the symmetric algebra of an ideal
description: scientific article; zbMATH DE number 3957255