J Austral Math Soc Ser A 58 pp287--297, 1995.
(Received 1 February 1992; revised 21 July 1992)
A module M is said to be weakly-injective if and only if for every finitely generated submodule N of the injective hull E(M) of M there exists a submodule X of E(M), isomorphic to M such that N Ì X. In this paper we investigate weakly-injective modules over bounded hereditary noetherian prime rings. In particular we show that torsion-free modules over bounded hnp rings are always weakly-injective, while torsion modules finite Goldie dimension are weakly-injective only if they are injective. As an application, we show that weakly-injective modules over bounded Dedekind prime rings have a decomposition as a direct sum of an injective module B, and a module C satisfying that if a simple module S is embeddable in C the the (external) direct sum of all proper submodules of the injective hull of S is also imbeddable in C. Indeed, we show that over a bounded hereditary noetherian prime ring every uniform module has periodicity one if and only if every weakly-injective mudule has such a decomposition.
1991 AMS Subject Classification: primary: 16A14, 16A52; secondary: 16A12, 16A33
Last Modified: Thu Jan 9 9:04:22 2003