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Galois extensions and subspaces of alternating bilinear forms with special rank properties (709).
| Content Provider | CiteSeerX |
|---|---|
| Author | Gow, Rod Quinlan, Rachel |
| Abstract | 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 ā 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 ā 1)/2, the rank of any non-zero element in the sum of the first k subspaces is at most nā2k+1. Slightly less sharp similar results hold for cyclic extensions of even degree. 1. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Non-zero Element Decomposition Theorem Vector Space First Subspace Galois Automorphisms Sharp Similar Result Direct Sum Main Result Cyclic Extension Odd Dimension Bilinear Form Cyclic Galois Extension Constant Rank |
| Content Type | Text |
| Resource Type | Article |
