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Localizations of Linked Quaternionic Mappings

Published online by Cambridge University Press:  20 November 2018

Joseph Yucas
Joseph Yucas*
Affiliation:
Southern Illinois University at Carbondale, Carbondale, Illinois
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Let G and B be abelian groups with G having exponent 2 and a distinguished element –1. In [7] we defined a linked quaternionic mapping to be a map q : G × G → B satisfying the following properties:

(A) q is symmetric and bilinear

(B) q(a, a) = q(a, – 1) for every a ∈ G, and

(L) q(a, b) = q(c, d) implies there exists x ∈ G such that q(a, b) = q(a, x) and q(c, d) = q(c, x).

A form (of dimension n over q) is a symbol φ = 〈a1, …, an〉 with a1, …, an ∈ G. The determinant and Hasse invariant of such a form φ are

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 1 , 01 February 1982 , pp. 247 - 256
Copyright
Copyright © Canadian Mathematical Society 1982

References

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7. Marshall, M. and Yucas, J., Linked quaternionic mappings and their associated Witt rings, Pacific J. Math. 95 (1981), 411–425.Google Scholar