Vol. 95, No. 2, 1981

Recent Issues
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Linked quaternionic mappings and their associated Witt rings

Murray Angus Marshall and Joseph Lewis Yucas

Vol. 95 (1981), No. 2, 411–425

A quaternionic mapping is a symmetric bilinear mapping q : G × G B, where G, B are Abelian groups, G has exponent 2 and contains a distinguished element 1 such that q(a,a) = q(a,1) a G. Such a mapping is said to be linked if q(a,b) = q(c,d) implies the existence of x G such that q(a,b) = q(a,x) and q(c,d) = q(c,x). The Witt ring W(q) of such a mapping q can be defined to be the integral group ring Z[G] factored by the ideal generated by 1 + (1) and the elements (a + b) (c + d) such that ab = cd and q(a,b) = q(c,d). If q is the quaternionic mapping associated to a field or semi-local ring A with 2 A, then q is linked, and W(q) is the Witt ring of free bilinear spaces over A. This paper gives a ring-theoretic description of the class of rings W(q), q linked. In particular, all such rings are shown to be strongly representational in the terminology of Kleinstein and Rosenberg.

Mathematical Subject Classification
Primary: 10C05, 10C05
Secondary: 10C01
Received: 9 August 1979
Revised: 14 April 1980
Published: 1 August 1981
Murray Angus Marshall
Joseph Lewis Yucas