Quadratic and Symmetric Bilinear Compositions of Quadratic Forms Over Commutative Rings

Abstract

Over commutative rings in which 2 is a zero-divisor, to compose a quadratic form with symmetric bilinear forms or with quadratic forms is not quite the same. In this article, the relation between the two classes of compositions is clarified and the results applied to find the ranks of minimal compositions.

Key Words:

• Bilinear forms
• Composition
• Quadratic forms

2000 Mathematics Subject Classification:

• 15A63
• 11E39
• 11E88

ACKNOWLEDGMENTS

I wish to express my gratitude to Prof. Max-Albert Knus, adviser of my diploma thesis, for a lot of support and inspiring discussions and also to Giordano Favi for corrections and helpful suggestions. Many thanks to the referee for all suggestions, especially for some simplifications in the proof of the Rank 6 Theorem.

Notes

Communicated by A. Elduque.