Tiled orders and Frobenius rings.
type: Item
instance of: scholarly article
title: Tiled orders and Frobenius rings.
zbMATH Open document ID: 1033.16006
DOI: 10.1023/A:1020563824196
author: Zh. T. Chernousova
author: Michael Dokuchaev
author: V. V. Kirichenko
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Let \(R\) be a discrete valuation ring with quotient field \(K\) and \({\mathfrak p}:=\text{Rad\,}R\). For an \(R\)-order \(\Lambda\) in a symmetric \(K\)-algebra \(A\), the \((\Lambda,\Lambda)\)-bimodules \(\Lambda\) and \(\Lambda^*:=\hom_R(\Lambda,R)\) can be regarded as full \(R\)-lattices in \(A\). Choose any \(n\in\mathbb{N}\) such that \({\mathfrak p}^n\Lambda^*\subset\text{Rad}^2\Lambda\) in \(A\). Then \(\Lambda/{\mathfrak p}^n\Lambda^*\) is a symmetric Artinian algebra with the same Gabriel quiver as \(\Lambda\). The authors prove this for tiled orders \(\Lambda\).
reviewed by: Wolfgang Rump
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16L60
zbMATH DE Number: 1928302
zbMATH Keywords: tiled orders
zbMATH Keywords: symmetric algebras
zbMATH Keywords: lattices
zbMATH Keywords: Gabriel quivers
MaRDI profile type: Publication
full work available at URL: a:1020563824196
OpenAlex ID: W24892312
description: scientific article; zbMATH DE number 1928302