Quasi-valuations -- topology and the weak approximation theorem
Shai Sarussi
Sce College, Ashdod, Israel
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Abstract
Suppose is a field with a nontrivial valuation and valuation ring , is a finite field extension and is a quasi-valuation on extending . We study the topology induced by . We prove that the quasi-valuation ring determines the topology, independent of the choice of its quasi-valuation. Moreover, we prove the weak approximation theorem for quasi-valuations.