scholarly journals Combinatorial techniques and abstract Witt rings III

1991 ◽  
Vol 148 (1) ◽  
pp. 39-58 ◽  
Author(s):  
Robert Fitzgerald
Keyword(s):  
Witt Rings

scholarly journals Crystal growth and Witt rings

1991 ◽  
Vol 136 (1) ◽  
pp. 190-196 ◽  
Author(s):  
Mieczysław Kula
Keyword(s):  
Crystal Growth ◽  
Witt Rings

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].

Witt rings of weakly orderable double loops and nearfields

1990 ◽  
Vol 17 (1-2) ◽  
pp. 106-119 ◽  
Author(s):  
Franz B. Kaihoff
Keyword(s):  
Witt Rings

scholarly journals On natural homomorphisms of Witt rings

2005 ◽  
Vol 133 (9) ◽  
pp. 2519-2523 ◽  
Author(s):  
Marzena Ciemała ◽  
Kazimierz Szymiczek
Keyword(s):  
Witt Rings

Witt rings as integral rings

1987 ◽  
Vol 90 (3) ◽  
pp. 631-633 ◽  
Author(s):  
D. W. Lewis
Keyword(s):  
Witt Rings

Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings

1978 ◽  
Vol 30 (4) ◽  
pp. 872-895 ◽  
Author(s):  
Jerrold L. Kleinstein ◽  
Alex Rosenberg
Keyword(s):  
Residue Class ◽  
Point Of View ◽  
Prime Ideals ◽  
Bilinear Forms ◽  
Semilocal Ring ◽  
Witt Ring ◽  
Witt Rings ◽  
Full Knowledge ◽  
Carry Over

This paper originated in an attempt to carry over the results of [3] from the case of a field of characteristic different from two to that of semilocal rings. To carry this out, we reverse the point of view of [3] and do assume a full knowledge of the theory of Witt rings of classes of nondegenerate symmetric bilinear forms over semilocal rings as given, for example, in [10; 11]. It turns out that the rings WT of [3] are just the residue class rings of W(C), the Witt ring of a semilocal ring C, modulo certain intersections of prime ideals.

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