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Decomposition of Witt Rings

Published online by Cambridge University Press:  20 November 2018

Andrew B. Carson  and
Murray A. Marshall
Andrew B. Carson
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
Murray A. Marshall
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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We take the definition of a Witt ring to be that given in [13], i.e., it is what is called a strongly representational Witt ring in [8]. The classical example is obtained by considering quadratic forms over a field of characteristic ≠ 2 [17], but Witt rings also arise in studying quadratic forms or symmetric bilinear forms over more general types of rings [5,7, 8, 9]. An interesting problem in the theory is that of classifying Witt rings in case the associated group G is finite. The reduced case, i.e., the case where the nilradical is trivial, is better understood. In particular, the above classification problem is completely solved in this case [4, 12, or 13, Corollary 6.25]. Thus, the emphasis here is on the non-reduced case. Although some of the results given here do not require |G| < ∞, they do require some finiteness assumption. Certainly, the main goal here is to understand the finite case, and in this sense this paper is a continuation of work started by the second author in [13, Chapter 5].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 6 , 01 December 1982 , pp. 1276 - 1302
Copyright
Copyright © Canadian Mathematical Society 1982

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