On nonsingularly k-primitive rings

Ann K. Boyle, M. G. Deshpande and Edmund H. Feller

Vol. 68 (1977), No. 2, 303–311

DOI: 10.2140/pjm.1977.68.303

Abstract

A ring R is called k-primitive if it has a faithful cyclic critical right module C with |C| = k. We first show that k-primitive rings with Krull dimension have many properties in common with prime rings. For the case where R is a PWD with a faithful critical right ideal, we obtain an internal characterization.

Mathematical Subject Classification

Primary: 16A46, 16A46

Milestones

Received: 24 March 1976

Revised: 22 November 1976

Published: 1 February 1977