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• W2015191305 abstract "Let K be a field admitting a cyclic Galois extension of degree n. The main result of this paper is a decomposition theorem for the space of alternating bilinear forms defined on a vector space of odd dimension n over K. We show that this space of forms is the direct sum of (n-1)/2 subspaces, each of dimension n, and the non-zero elements in each subspace have constant rank defined in terms of the orders of the Galois automorphisms. Furthermore, if ordered correctly, for each integer k lying between 1 and (n-1)/2, the rank of any non-zero element in the sum of the first k subspaces is at most n-2k+1. Slightly less sharp similar results hold for cyclic extensions of even degree." @default.
• W2015191305 created "2016-06-24" @default.
• W2015191305 creator A5015933130 @default.
• W2015191305 creator A5062948487 @default.
• W2015191305 date "2009-04-01" @default.
• W2015191305 modified "2023-10-02" @default.
• W2015191305 title "Galois extensions and subspaces of alternating bilinear forms with special rank properties" @default.
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• W2015191305 doi "https://doi.org/10.1016/j.laa.2008.11.021" @default.
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