The descending chain condition relative to a torsion theory

Robert Wilmer Miller and Mark Lawrence Teply

Vol. 83 (1979), No. 1, 207–219

DOI: 10.2140/pjm.1979.83.207

Abstract

A well-known theorem of Hopkins and Levitzki states that any left artinian ring with identity element is left noetherian. The main theorem of this paper generalizes this to the situation of a hereditary torsion theory with associated idempotent kernel functor σ. It is shown that if a ring R with identity element has the descending chain condition on σ-closed left ideals, then R has the ascending chain condition on σ-closed left ideals.

Mathematical Subject Classification

Primary: 16A63, 16A63

Secondary: 16A08

Milestones

Received: 31 August 1977

Revised: 21 September 1977

Published: 1 July 1979