Fields for which the projective Schur subgroup is the whole Brauer group
type: Item
instance of: scholarly article
title: Fields for which the projective Schur subgroup is the whole Brauer group
zbMATH Open document ID: 1015.16013
DOI: 10.1007/BF02785867
author: Eli Aljadeff
author: Jack Sonn
published in: Israel Journal of Mathematics
publication date: 2003-01-26T00:00:00Z
review text: The authors prove that if \(K\) is a finitely generated infinite field, then the Brauer group of \(K\) equals the projective Schur subgroup of \(K\) if and only if \(K\) is a global field. Moreover, if \(K( (t))\) is the field of formal power series in \(t\) over \(K\) (again a finitely generated infinite field), then the Brauer group of \(K( (t))\) equals the projective Schur subgroup of \(K( (t))\) if and only if \(K=\mathbb{Q}\).
Mathematics Subject Classification ID: 16K50
Mathematics Subject Classification ID: 12G05
zbMATH DE Number: 1850619
zbMATH Keywords: finitely generated infinite fields
zbMATH Keywords: Brauer groups
zbMATH Keywords: projective Schur subgroups
zbMATH Keywords: global fields
zbMATH Keywords: fields of formal power series
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
cites work: Projective Schur algebras have Abelian splitting fields
cites work: On the projective Schur group of a field
cites work: Projective Schur algebras of nilpotent type are Brauer equivalent to radical algebras
cites work: Exponent reduction for radical Abelian algebras
cites work: Exponent reduction for projective Schur algebras
cites work: Relative Brauer groups and \(m\)-torsion
cites work: Projective Schur groups of iterated power series fields.
cites work: Q3922829
cites work: Q3027108
cites work: Einfache Algebren und projektive Darstellungen über Zahlkörpern
cites work: Q4263461
cites work: Q4126536
cites work: Q3856855
full work available at URL: https://doi.org/10.1007/bf02785867
OpenAlex ID: W2135273054
Recommended article: On the projective Schur group of a field
Recommended article: The projective Schur subgroup of the Brauer group and root groups of finite groups
Recommended article: Projective Schur groups of Henselian fields
Recommended article: The Schur subgroup of the Brauer group of a local field
Recommended article: Q3804807
Recommended article: Brauer groups of fields
Recommended article: Q3996577
Recommended article: Q4691728
Recommended article: Q5447922
description: scientific article; zbMATH DE number 1850619