Commutative rings whose homomorphic images are self-injective

Lawrence S. Levy

Vol. 18 (1966), No. 1, 149–153

DOI: 10.2140/pjm.1966.18.149

Abstract

Dedekind domains are characterized among integral domains by the property that every ideal be a projective module. The most naive dual characterization—that every homomorphic image of R be an injective module—is false. In fact, a domain with this property would have to be a field. An injectivity property that works, in the noetherian case, is the property that every proper homomorphic image be a self-injective ring. The main result of this note is:

Mathematical Subject Classification

Primary: 13.15

Secondary: 13.40

Milestones

Received: 26 February 1965

Published: 1 July 1966