| Texto completo | |
| Autor(es): |
Ferreira, Mauricio A.
;
Wadsworth, Adrian R.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 368, n. 3, p. 54-pg., 2016-03-01. |
| Resumo | |
In this paper we prove relationships between two generalizations of commutative valuation theory for noncommutative central simple algebras: (1) Dubrovin valuation rings; and (2) the value functions called gauges introduced by Tignol and Wadsworth. We show that if v is a valuation on a field F with associated valuation ring V and v is defectless in a central simple F-algebra A, and C is a subring of A, then the following are equivalent: (a) C is the gauge ring of some minimal v-gauge on A, i.e., a gauge with the minimal number of simple components of C/J(C); (b) C is integral over V with C = B-1 boolean AND ... boolean AND B-xi where each B-i is a Dubrovin valuation ring of A with center V, and the B-i satisfy Grater's Intersection Property. Along the way we prove the existence of minimal gauges whenever possible and we show how gauges on simple algebras are built from gauges on central simple algebras. (AU) | |
| Processo FAPESP: | 06/00157-3 - Relacionando propriedades de natureza aritmetico-geometricas de um corpo com características do grupo total de Galois do corpo |
| Beneficiário: | Maurício de Araujo Ferreira |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |