Vol. 48, No. 1, 1973

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A topological characterization of complete, discretely valued fields

Seth Warner

Vol. 48 (1973), No. 1, 293–298

It is shown that the topology of a topological field F is given by a complete, discrete valuation if and only if F is locally strictly Iinearly compact. More generally, the topology of a topological division ring K is given by a complete, discrete valuation and K is finite dimensional over its center if and only if K is locally centrally linearly compact, that is, if and only if K contains an open subring B, the open left ideals of which form a fundamental system of neighborhoods of zero, such that B, regarded as a module over its center, is strictly linearly compact.

Mathematical Subject Classification 2000
Primary: 12J10
Received: 12 June 1972
Published: 1 September 1973
Seth Warner