Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 22 Issue 1
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- Pages.11-15
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- 1985
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
CLASSIFICATION OF CLIFFORD ALGEBRAS OF FREE QUADRATIC SPACES OVER FULL RINGS
Abstract
Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho
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