Every module is an inverse limit of injective modules

Abstract

It is shown that any left module A over a ring R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives. If R is left Noetherian, A can also be written as the inverse limit of a system of surjective homomorphisms of injectives. Some questions are raised.

5 pages. In revised version, "Lemma 8" has become "Corollary 9"; the new Lemma 8 gives a general argument underlying the old one. Other changes are mainly improvements in wording etc

Cited by in corpus (1)

• Closure properties of $\underrightarrow{\lim }\mathcal{C}$