A property of independent elements
type: Item
instance of: scholarly article
title: A property of independent elements
zbMATH Open document ID: 0574.13002
DOI: 10.1016/0022-4049(85)90015-5
author: Christer Lech
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: The elements \(x_ 1,x_ 2,...,x_ k\) in a commutative ring are called independent if \(x_ 1r_ 1+x_ 2r_ 2+...+x_ kr_ k=0\) implies that \(r_ 1,r_ 2,...,r_ k\) belongs to \((x_ 1,x_ 2,...,x_ k)\). The paper consists of an elegant proof of the following theorem: A set of independent elements cannot be contained in a proper ideal generated by fewer elements. As a corollary one has the following (well-known) result: For any local flat morphism \(A\to B\) of Noetherian rings, emb.dim \(A\leq emb.\dim B\).
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 13C15
zbMATH DE Number: 3916421
zbMATH Keywords: independent elements
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90015-5
OpenAlex ID: W1966300127
cites work: Q3344077
cites work: Inequalities related to certain couples of local rings
cites work: Ideals generated by \(R\)-sequences
description: scientific article; zbMATH DE number 3916421