Cancellation of finitely generated modules over regular rings
type: Item
instance of: scholarly article
title: Cancellation of finitely generated modules over regular rings
zbMATH Open document ID: 0716.16007
author: Kenneth R. Goodearl
author: Jaume Moncasi
published in: Osaka Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: In this note we show that if R is a regular ring which is \(N^*\)- complete, or right or left \(\aleph_ 0\)-continuous, or left \(\aleph_ 0\)-injective, then every finitely generated right R-module cancels from direct sums if and only if R has bounded index of nilpotency (and so all primitive factor rings of R are artinian). As an application we also obtain a characterization of those polynomial rings R[x] that are semihereditary in the case that R is either \(N^*\)-complete or right or left \(\aleph_ 0\)-continuous.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16E60
Mathematics Subject Classification ID: 16W60
zbMATH DE Number: 4179575
zbMATH Keywords: regular ring
zbMATH Keywords: \(N^ *\)-complete
zbMATH Keywords: left \(\aleph _ 0\)-continuous
zbMATH Keywords: left \(\aleph _ 0\)-injective
zbMATH Keywords: finitely generated right R-module
zbMATH Keywords: direct sums
zbMATH Keywords: bounded index of nilpotency
zbMATH Keywords: primitive factor rings
zbMATH Keywords: semihereditary
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4179575