Topologies on the ring of integers of a global field

Jo-Ann Deborah Cohen

Vol. 93 (1981), No. 2, 269–276

DOI: 10.2140/pjm.1981.93.269

Abstract

A characterization of all nondiscrete, locally bounded ring topologies on the ring of integers of an algebraic number field and all those on the ring of integers of an algebraic function field for which the field of constants is bounded is given. As a consequence of these results we obtain Mahler’s classic description of the seminorms on the ring of integers of an algebraic number field.

Mathematical Subject Classification 2000

Primary: 12J05

Milestones

Received: 14 November 1979

Revised: 23 January 1980

Published: 1 April 1981