Valuations on Algebras with Involution
| dc.creator | Tignol, J. -P. | |
| dc.creator | Wadsworth, A. R. | |
| dc.date | 2009-02-05 | |
| dc.date.accessioned | 2026-07-07T12:38:12Z | |
| dc.date.available | 2026-07-07T12:38:12Z | |
| dc.description | Let A be a central simple algebra with involution sigma of first or second kind. Let v be a valuation on the sigma-fixed part F of Z(A). A sigma-special v-gauge g on A is a kind of value function on A extending v on F, such that g(sigma(x) x) = 2g(x) for all x in A. It is shown (under certain restrictions if the residue characteristic is 2) that if v is Henselian, then there is a sigma-special v-gauge g if and only if sigma is anisotropic, and g is unique. If v is not Henselian, it is shown that there is a sigma-special v-gauge g if and only if sigma remains anisotropic after scalar extension from F to the Henselization of F re v; when this occurs, g is the unique sigma-invariant v-gauge on A. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0902.0849 | |
| dc.identifier | http://arxiv.org/abs/0902.0849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218675 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W10 (Primary) 16K20, 16W60, 16W50, 11E39 (Secondary) | |
| dc.title | Valuations on Algebras with Involution | |
| dc.type | text |