Galois extensions and subspaces of bilinear forms with special rank properties
| dc.creator | Gow, Rod | |
| dc.creator | Quinlan, Rachel | |
| dc.date | 2007-09-05 | |
| dc.date.accessioned | 2026-07-07T08:27:51Z | |
| dc.date.available | 2026-07-07T08:27:51Z | |
| dc.description | 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. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0709.0741 | |
| dc.identifier | http://arxiv.org/abs/0709.0741 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137414 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 15A63, 12F10, 11E39 | |
| dc.title | Galois extensions and subspaces of bilinear forms with special rank properties | |
| dc.type | text |