A classification theorem for quadratic forms over semi-local rings

Joseph L. Yucas

Published: 1986-09-30

Vol. 2 (1986)

A classification theorem for quadratic forms over semi-local rings

Joseph L. Yucas

Abstract

Let R be a semi-local ring with 2∈U(R) and such that all residue class fields of R contain more than 3 elements. It is proved here that bilinear spaces over R are classified by dimension, determinant, Hasse invariant and total signature if and only if the third power of the fundamental ideal of Witt ring W(R) is torsion free. This is a generalization of the same result when R is a field due to Elman and Lam.

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Yucas, J. L. (1986). A classification theorem for quadratic forms over semi-local rings. Annales Mathematicae Silesianae, 2, 7–12. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14313

References

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Vol. 2 (1986)
Published: 1986-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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