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Schur and Projective Schur Groups of Number Rings

Published online by Cambridge University Press:  20 November 2018

Peter Nelis
Peter Nelis*
Affiliation:
Department of Mathematics University of Antwerp, U.I.A. 2610 Antwerp, Belgium
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The Schur or projective Schur group of a field consists of the classes of central simple algebras which occur in the decomposition of a group algebra or a twisted group algebra. For number fields, the projective Schur group has been determined in [8], whereas the Schur group is extensively studied in [25]. Recently, some authors have generalized these concepts to commutative rings. One then studies the classes of Azumaya algebras which are epimorphic images of a group ring or a twisted group ring. Though several properties of the Schur or projective Schur group defined in this way have been obtained, they remain rather obscure objects.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 540 - 558
Copyright
Copyright © Canadian Mathematical Society 1991

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