Every module is an inverse limit of injective modules

Details Every module is an inverse limit of injective modules Every module is an inverse limit of injective modules

2011-04-15

arxiv.org/abs/1104.3173v2

Mathematics

Rings and Algebras

5 pages. In revised version, "Lemma 8" has become "Corollary 9"; the new Lemma 8 gives a general argument underlying the old o

Scientific paper

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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