Injective modules over duo rings

Thomas Stephen Shores

Vol. 40 (1972), No. 3, 695–702

DOI: 10.2140/pjm.1972.40.695

Abstract

Let R be a ring with unit whose right and left ideals are two-sided ideals. It is shown that every Noetherian injective R-module has finite length (i.e., has a finite composition series). If I is a maximal ideal of R, then R has a universal localization, R_I at I. The condition that the injective hull of R∕I is finite is characterized in terms of R_I.

Mathematical Subject Classification

Primary: 16A52

Milestones

Received: 12 April 1971

Published: 1 March 1972