Value functions on central simple algebras

Morandi, Patrick J.

doi:10.1090/S0002-9947-1989-0986697-6

Value functions on central simple algebras
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Trans. Amer. Math. Soc. 315 (1989), 605-622 Request permission

Abstract:

In this paper we study noncommutative valuation rings as defined by Dubrovin. While there is in general no valuation associated to a Dubrovin valuation ring, we show that there is a value function associated to any Dubrovin valuation ring integral over its center. By using value functions we obtain information on Dubrovin valuation rings in a tensor product, both generalizing and giving a much simpler proof of a result about valued division algebras. By being able to work directly with central simple algebras we gain new information about division algebras over Henselian fields.

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