Modules and quadratic forms over polynomial algebras

Knus, M.-A.; Ojanguren, M.

doi:10.1090/S0002-9939-1977-0498534-4

Modules and quadratic forms over polynomial algebras
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by M.-A. Knus and M. Ojanguren PDF

Proc. Amer. Math. Soc. 66 (1977), 223-226 Request permission

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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