The Witt ring

1982 ◽  
pp. 12-46
Author(s):  
Max L. Warshauer
Keyword(s):  
Witt Ring

scholarly journals Annihilating polynomials for quadratic forms

2001 ◽  
Vol 27 (7) ◽  
pp. 449-455 ◽  
Author(s):  
David W. Lewis
Keyword(s):  
Quadratic Forms ◽  
Witt Ring ◽  
Short Survey

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field.

The Witt Ring of a Space of Ordering

1980 ◽  
Vol 258 (2) ◽  
pp. 505 ◽  
Author(s):  
Murray Marshall
Keyword(s):  
Witt Ring

Witt ring

2017 ◽  
pp. 191-206
Author(s):  
Kazimierz Szymiczek
Keyword(s):  
Witt Ring

scholarly journals The graded Witt ring and Galois cohomology. II

1989 ◽  
Vol 314 (2) ◽  
pp. 745-745 ◽  
Author(s):  
J{ón Kr. Arason ◽  
Richard Elman ◽  
Bill Jacob
Keyword(s):  
Galois Cohomology ◽  
Witt Ring

Graded Witt ring and unramified cohomology

K-Theory ◽  
1992 ◽  
Vol 6 (1) ◽  
pp. 29-44 ◽  
Author(s):  
R. Parimala ◽  
R. Sridharan
Keyword(s):  
Witt Ring ◽  
Unramified Cohomology

Basic facts about symmetric bilinear forms, and definition of the Witt ring

Wittrings ◽  
1982 ◽  
pp. 1-18
Author(s):  
Manfred Knebusch ◽  
Manfred Kolster
Keyword(s):  
Bilinear Forms ◽  
Witt Ring ◽  
Basic Facts ◽  
Definition Of

Quotients and Inverse Limits of Spaces of Orderings

1979 ◽  
Vol 31 (3) ◽  
pp. 604-616 ◽  
Author(s):  
Murray A. Marshall
Keyword(s):  
Quadratic Forms ◽  
Sums Of Squares ◽  
Inverse Limits ◽  
Witt Ring ◽  
Spaces Of Orderings ◽  
Image Position

A connection between the theory of quadratic forms defined over a given field F, and the space XF of all orderings of F is developed by A. Pfister in [12]. XF can be viewed as a set of characters acting on the group F×/ΣF×2, where ΣF×2 denotes the subgroup of F× consisting of sums of squares. Namely, each ordering P ∈ XF can be identified with the characterdefined byIt follows from Pfister's result that the Witt ring of F modulo its radical is completely determined by the pair (XF, F×/ΣF×2).

Decomposition of Witt Rings

1982 ◽  
Vol 34 (6) ◽  
pp. 1276-1302 ◽  
Author(s):  
Andrew B. Carson ◽  
Murray A. Marshall
Keyword(s):  
Quadratic Forms ◽  
Classification Problem ◽  
Bilinear Forms ◽  
Interesting Problem ◽  
Witt Ring ◽  
Witt Rings ◽  
Finite Case ◽  
Characteristic 2 ◽  
Definition Of

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].

Real cohomology and the powers of the fundamental ideal in the Witt ring

2017 ◽  
Vol 2 (3) ◽  
pp. 357-385 ◽  
Author(s):  
Jeremy Jacobson
Keyword(s):  
Witt Ring ◽  
Fundamental Ideal

scholarly journals The Witt ring of a full ring

1980 ◽  
Vol 64 (1) ◽  
pp. 148-166 ◽  
Author(s):  
B. Kirkwood ◽  
B.R. McDonald
Keyword(s):  
Witt Ring
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