Artin rings of global dimension two
type: Item
instance of: scholarly article
title: Artin rings of global dimension two
zbMATH Open document ID: 0549.16015
DOI: 10.1016/0021-8693(85)90127-9
author: William H. Gustafson
author: Dan Zacharia
author: E. L. Green
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let R be a basic left Artin ring of global dimension at most two and with n isomorphism classes of simple left R-modules. In the paper one shows in a combinatorial way that R has Loewy length at most \(2^ n-1\) and there are no loops in the ordinary quiver of R.
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16Exx
zbMATH DE Number: 3875478
zbMATH Keywords: basic left Artin ring
zbMATH Keywords: global dimension
zbMATH Keywords: simple left R-modules
zbMATH Keywords: Loewy length
reviewed by: Andrzej Skowroński
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90127-9
OpenAlex ID: W2070625827
cites work: Modules with decompositions that complement direct summands
cites work: Q4097440
cites work: Treue einfach zusammenhaengende Algebren. I
cites work: Q3240881
cites work: Q4071921
cites work: Radical layers of representable functors
cites work: On the Cartan matrix of an Artin algebra of global dimension two
description: scientific article; zbMATH DE number 3875478