Every module is an inverse limit of injectives

Bergman, George

doi:10.1090/S0002-9939-2012-11453-4

Every module is an inverse limit of injectives
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Proc. Amer. Math. Soc. 141 (2013), 1177-1183 Request permission

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.

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