Rings where the annihilators of α-critical modules are prime ideals

Edmund H. Feller

Vol. 93 (1981), No. 2, 299–306

DOI: 10.2140/pjm.1981.93.299

Abstract

For a ring R with Krull dimension α, we investigate the property that the annihilators of α-critical modules are prime ideals. If R satisfies the large condition then this property holds iff R∕I₀ is semiprime, where I₀ is the maximal right ideal of Krull dimension < α. The property holds in the following rings, (i) R is weakly ideal invariant, (ii) R satisfies the left AR property, or (iii) the prime ideals of R are right localizable. In addition, if R is a hereditary Noetherian α-primitive ring, then R is a prime ring.

Mathematical Subject Classification

Primary: 16A55, 16A55

Milestones

Received: 5 March 1980

Published: 1 April 1981