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Division Graded Algebras in the Brauer-Wall Group

Published online by Cambridge University Press:  20 November 2018

Francis Coghlan  and
Peter Hoffman
Francis Coghlan
Affiliation:
Mathematics Department, Manchester University, Manchester, England, M13 9PL
Peter Hoffman
Affiliation:
Pure Mathematics Department, Waterloo, Ontario, N2L 3G1
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Abstract

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We show that every element in the Brauer-Wall group of a field with characteristic different from 2 is represented uniquely by a division graded algebra, (i.e. homogeneous elements are invertible) but, of course, not necessarily by a graded (division algebra). This is a fairly direct consequence of Wall's structure theory for central simple Z/2-graded algebras.

Keywords

13A20graded algebradivision algebraBrauer-Wall group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 21 - 24
Copyright
Copyright © Canadian Mathematical Society 1995

References

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[W] Wall, C. T. C., Graded Brauer Groups, J. Reine Angew. Math. 213(1964), 187–199.Google Scholar