The elementary action on unimodular rows over a monoid ring. II
type: Item
instance of: scholarly article
title: The elementary action on unimodular rows over a monoid ring. II
zbMATH Open document ID: 0813.20075
author: Joseph Gubeladze
published in: Journal of Algebra
publication date: 1993-05-16T00:00:00Z
review text: Let \(R\) be a commutative Noetherian ring with finite Krull dimension \(d\) and \(M\) an additive submonoid of \(\mathbb{Q}^ r_ +\) for some \(r \geq 1\). In part I [J. Algebra 148, 135-161 (1992; Zbl 0795.20056)], the author showed that when \(M \subset \mathbb{Q}^ r_ +\) is an integral extension, the group \(E_ n(R[M])\) of elementary matrices acts transitively on the set \(Um_ n (R[M])\) of unimodular rows of all \(n \geq \max(d+2,3)\). In this paper, the author extends this result to the class of submonoids of \(\mathbb{Q}^ r_ +\) of \(\Phi\)-simplicial growth, i.e., those monoids \(M\) which admit a sequence of finite convex polyhedra \(P_ 1 \subset P_ 2 \subset \dots \subset P_ k = \Phi(M)\) such that \(P_ 1\) and the closures (in the sense of Euclidean metric) of \(P_{i + 1} - P_ i\) are simplices for each \(1 \leq i \leq k - 1\).
reviewed by: David F. Anderson
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 19A13
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 13C10
zbMATH DE Number: 168185
zbMATH Keywords: monoid rings
zbMATH Keywords: commutative Noetherian ring
zbMATH Keywords: Krull dimension
zbMATH Keywords: elementary matrices
zbMATH Keywords: unimodular rows
zbMATH Keywords: \(\Phi\)-simplicial growth
zbMATH Keywords: finite convex polyhedra
MaRDI profile type: Publication
full work available at URL: jabr.1993.1038
OpenAlex ID: W4212798384
DOI: 10.1006/JABR.1993.1038
description: scientific article; zbMATH DE number 168185