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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Modules and quadratic forms over polynomial algebras


Authors: M.-A. Knus and M. Ojanguren
Journal: Proc. Amer. Math. Soc. 66 (1977), 223-226
MSC: Primary 13F20; Secondary 15A63
MathSciNet review: 0498534
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Abstract: Let D be a finite dimensional division algebra over a field k. Projective $ D[x,y]$-modules of rank $ \geqslant 2$ are free. Projective ideals of $ D[x,y]$, D a quaternionic division algebra, which are not free, are used to construct regular quadratic $ k[x,y]$-modules which are not extended from k.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0498534-4
PII: S 0002-9939(1977)0498534-4
Article copyright: © Copyright 1977 American Mathematical Society