Realizations of finite dimensional algebras over the rationals
type: Item
instance of: scholarly article
title: Realizations of finite dimensional algebras over the rationals
zbMATH Open document ID: 0831.20072
author: W. J. Wickless
author: Charles Vinsonhaler
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-02-06T00:00:00Z
review text: The authors recall the well-known realization problem in Abelian group theory: when can a given ring \(R\) be realized as an endomorphism ring \(\text{End }G\) of an Abelian group \(G\) of a certain kind? Then a specific form of the realization problem is considered: when can a \(Q\)-algebra \(A\subset\text{End }V\) where \(V\) is a finite-dimensional vector space over the field of rationals \(Q\) be represented as \(A=Q\text{ End }G\) where \(G\) is an additive subgroup in \(V\) with \(QG=V\). The ring \(\text{End }G\) is commonly associated here with a subring in \(\text{End }V\).
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 757789
zbMATH Keywords: realizations as endomorphism rings
zbMATH Keywords: realization problem
zbMATH Keywords: Abelian groups
zbMATH Keywords: finite-dimensional vector spaces
reviewed by: I. Kh. Bekker
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072357
OpenAlex ID: W2009826025
cites work: The flat dimension of mixed abelian groups as \(E\)-modules
cites work: On Locally Free Torsion-Free Rings of Finite Rank
cites work: Q3726220
cites work: Regular and principal projective endomorphism rings of mixed abelian groups
cites work: Q3140877
cites work: Homomorphisms and duality for torsion-free groups
DOI: 10.1216/RMJM/1181072357
description: scientific article; zbMATH DE number 757789