Quadratic forms over Quadratic Extensions of Fields with Two Quaternion Algebras
1979 ◽
Vol 31
(5)
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pp. 1047-1058
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Keyword(s):
The Real
◽
In this paper, we analyze what happens with respect to quadratic forms when a square root is adjoined to a field F which has exactly two quaternion algebras. There are many such fields—the real numbers and finite extensions of the p-adic numbers being two familiar examples. For general quadratic extensions, there are many unanswered questions concerning the quadratic form structure, but for these special fields we can clear up most of them.It is assumed char F ≠ 2 and K = F (√a) where a ∊ Ḟ – Ḟ2. Ḟ denotes the non-zero elements of F. Generally the letters a, b, c, … and α, β, … refer to elements from Ḟ and x, y, z, … come from .
1961 ◽
Vol 57
(3)
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pp. 507-515
Keyword(s):
1981 ◽
Vol 89
(2)
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pp. 225-235
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1981 ◽
Vol 31
(2)
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pp. 175-188
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1983 ◽
Vol 94
(1)
◽
pp. 1-8
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Keyword(s):
1980 ◽
Vol 29
(4)
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pp. 439-453
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1968 ◽
Vol 8
(1)
◽
pp. 87-101
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Keyword(s):