Filtrations and valuations on rings

Helen Elizabeth. Adams

Vol. 43 (1972), No. 1, 7–14

DOI: 10.2140/pjm.1972.43.7

Abstract

The concept of a multiplicative filtration on a ring is generalized so as to include among filtered rings, rings with valuation, pseudovaluation and semivaluation. The generalized filtration induces a topology on the ring, and it is shown that the Hausdorff completion of the resulting topological ring can be described by an inverse limit. The paper finishes with an example illustrating the theory.

Mathematical Subject Classification

Primary: 16A80

Milestones

Received: 2 April 1971

Revised: 30 September 1971

Published: 1 October 1972