Vol. 69, No. 1, 1977

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Pairs of symmetric bilinear forms in characteristic 2

William Charles Waterhouse

Vol. 69 (1977), No. 1, 275–283

The Grothendieck group of finite-length inner product modules over a PID is here shown to be a sum of countably many copies of the corresponding groups for the residue fields. It follows that nonsingular pairs of symmetric bilinear forms in characteristic 2 owe their extra complexity only to lack of a cancellation theorem: The invariants for isometry in other characteristics continue to determine classes in the Grothendieck group. This is also true for singular pairs.

Mathematical Subject Classification 2000
Primary: 10C05, 10C05
Secondary: 15A63
Received: 6 July 1976
Published: 1 March 1977
William Charles Waterhouse