Every module is an inverse limit of injective modules
Rings and Algebras
2013-05-10 v2
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.
Keywords
Cite
@article{arxiv.1104.3173,
title = {Every module is an inverse limit of injective modules},
author = {George M. Bergman},
journal= {arXiv preprint arXiv:1104.3173},
year = {2013}
}
Comments
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