Abstract Quadratic Forms

Canadian Journal of Mathematics - Tập 21 - Trang 1218-1233 - 1969
Irving Kaplansky1, R. J. Shaker1
1University of Chicago, Chicago, Illinois

Tóm tắt

We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence relation on unordered n-ples of G. For n = 2: (a, b) ~ (c, d) if a + b = c + d and ab = cd. For n > 2 we define equivalence “piecewise”: there is to be a chain from (a1, …, an) to (b1, …, bn) where at each step only two elements are changed in accordance with the equivalence just defined for n = 2.

Từ khóa


Tài liệu tham khảo

Scharlau, 1967, Invent. Math., Quadratische Formen und Galois-Cohomologie, 4, 238

Witt, 1937, J. Reine Angew. Math., Théorie der quadratischen Formen in beliebigen Kôrpern, 176, 31

Shaker, 1968, Abstract quadratic forms

Knight, 1966, Proc. Cambridge Philos. Soc., Quadratic forms over R(t), 62, 197

Albert, 1938, Trans. Amer. Math- Soc., Symmetric and alternate matrices in an arbitrary field, 43, 386

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Thông tin xuất bản

Canadian Journal of Mathematics

Tập 21

1218-1233

Thông tin tác giả