Um estudo topologico sobre aneis de valorização de Dubrovin
AUTOR(ES)
Oscar Ricardo Janesch
DATA DE PUBLICAÇÃO
1998
RESUMO
Dubrovin valuation rings in simple artinian rings are studied topologically. The motivation is the Theorem due to Kowalski and Dürbaum which ensures that any V-topology over a field is generated by means of a valuation ring or an absolute value of the field. Beginning from Dubrovin valuation ring R in the simple artinian ring Q, a topology namely R-ideal topology is defined. Properties of the R-ideal topology are proved, and this topology is connected with J(R)-adic topology, and also with the topology produced by a value function in ring Q. The concept of V-topology for artinian simple ring is introducted in order to obtain a classification of V-topologies in Q. These V-topologies are generated exactly by Dubrovin valuation rings or norms in Q. It is also shown that every V-topology in Q is locally bounded. The topologies generated by Dubrovin valuation rings in Q are characterized through locally bounded topologies with a bounded neighbourhood of zero that is closed by sums, and the restriction of this topology over your center is a V-topogical field
ASSUNTO(S)
teoria de valorização aneis não-comutativos
