Valuations and group algebras
type: Item
instance of: scholarly article
title: Valuations and group algebras
zbMATH Open document ID: 0920.16014
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-07-11T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108464
review text: This paper discusses localization in group rings and crossed products of left ordered groups. To do this, the authors consider the following structure: (1) pairs \((\Gamma_1,\Pi_1)\) and \((\Gamma_2,\Pi_2)\) where \(\Pi_i\) is the positive cone of the left ordered group \(\Gamma_i\); (2) a subsemigroup \(\Delta\) of \(\Gamma_1\) containing \(\Pi_1\) and a cone preserving semigroup morphism \(\phi\colon\Delta\to\Gamma_2\). Since left ordered groups are unique product groups, the results of this paper concerning units, isomorphism questions and the Jacobson radical of crossed products are all well known.
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 16W60
zbMATH DE Number: 1279129
zbMATH Keywords: group algebras
zbMATH Keywords: crossed products
zbMATH Keywords: left ordered groups
zbMATH Keywords: localizations of group rings
zbMATH Keywords: unique product groups
author: Ulrich F. Albrecht
author: Günter Törner
reviewed by: D. S. Passman
MaRDI profile type: Publication
cites work: Group rings and generalized valuations
cites work: Q3325883
cites work: Torsion-free Abelian Groups, Valuations and Twisted Group Rings
cites work: Right-ordered groups
cites work: RATIONAL CLOSURES OF GROUP RINGS OF LEFT-ORDERED GROUPS
cites work: Q4104083
cites work: Bewertungen nicht kommutativer Körper
cites work: On Ordered Division Rings
description: scientific article; zbMATH DE number 1279129