On the corestriction of central simple algebras
type: Item
instance of: scholarly article
title: On the corestriction of central simple algebras
zbMATH Open document ID: 0595.16012
DOI: 10.1007/BF01161974
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173833
review text: This paper provides algebra-theoretic proofs for the following well-known results: (1) if L/K is a separable extension of fields of rank d and C is a central simple algebra over K, then \(cor_{L/K}(C\otimes L)\sim C^{\otimes d}\); (2) if L/K is a finite separable extension of fields and if a, b are non-zero elements of L and K respectively, then for any integer n such that K contains a primitive root of unitary \(\zeta\), the corestriction of the symbol algebra \((a,b)_ L\) of degree n (i.e. the central simple L-algebra generated by two elements u, v subject to the relations \(u^ n=a\), \(v^ n=b\), \(uv=\zeta vu)\) is similar to the symbol algebra \((N_{L/K}(a),b)/K\); i.e. \(cor_{L/K}(a,b)_ L\sim (N_{L/K}(a),b)_ K\) (projection formula). An error in \textit{P. Draxl}'s book: Skew fields (1983; Zbl 0498.16015) is thus corrected.
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 14F22
zbMATH DE Number: 3957350
zbMATH Keywords: separable extension of fields
zbMATH Keywords: central simple algebra
zbMATH Keywords: corestriction
zbMATH Keywords: symbol algebra
zbMATH Keywords: Brauer groups
author: Jean-Pierre Tignol
MaRDI profile type: Publication
cites work: The Sequential Design of Experiments for Infinitely Many States of Nature
cites work: Q3963168
cites work: On central simple algebras of given exponent
cites work: The corestriction of algebraic structures
cites work: The Brauer Group is Torsion
description: scientific article; zbMATH DE number 3957350