A tiled order having large global dimension
type: Item
instance of: scholarly article
title: A tiled order having large global dimension
zbMATH Open document ID: 0877.16008
author: Willem S. Jansen
author: Charles J. Odenthal
published in: Journal of Algebra
publication date: 1997-11-27T00:00:00Z
review text: For a discrete valuation domain \(R\) with quotient field \(K\), and any even integer \(N\geq 8\), a tiled \(R\)-order \(\Lambda_N\) in \(M_N(K)\) of global dimension \(2N-8\) is constructed. If \(P_1,\dots,P_N\) are the indecomposable projective right \(\Lambda_N\)-modules, the authors first prove that all the syzygies of \(\text{rad }P_{N-1}\) and \(\text{rad }P_N\) decompose into irreducible \(\Lambda_N\)-representations. Therefore, the projective dimension of these modules is easy to compute. In this way, a family of \(\Lambda_N\)-modules with known projective dimensions is obtained. The other direct summands of \(\text{Rad }\Lambda_N\) are then related to these modules by certain short exact sequences, and thus the global dimension of \(\Lambda_N\) is evaluated.
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 1038258
zbMATH Keywords: tiled orders
zbMATH Keywords: global dimension
zbMATH Keywords: indecomposable projective right modules
zbMATH Keywords: syzygies
zbMATH Keywords: projective dimension
zbMATH Keywords: exact sequences
reviewed by: Wolfgang Rump
MaRDI profile type: Publication
full work available at URL: jabr.1996.6928
OpenAlex ID: W2089138995
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DOI: 10.1006/JABR.1996.6928
description: scientific article; zbMATH DE number 1038258