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Exterior powers of fields and subfields

Published online by Cambridge University Press:  22 January 2016

David J. Saltman*
Affiliation:
Department of Mathematics, Yale University, New Haven, Connecticut 06520, USA
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Let D be a division algebra of finite dimension n2 over it’s center F. Suppose D has an involution, τ, of the first kind, of symplectic type (e.g. [1], p. 169). By the theory of the pfaffian, τ symmetric elements have degree less than n/2 over F. On the other hand, Tamagawa has shown (unpublished) that involutions like τ are closely related to minimal symmetric idempotents in DF D. This author began by examining and trying to generalize these relationships. But before any theory seemed possible for division algebras, a theory relating subfields and symmetric idempotents was required. This investigation gave rise to the results presented here, especially the main theorem in Section Two.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[ 1 ] Rowen, L., Polynomial Identities in Ring Theory, Academic Press, New York 1980.Google Scholar