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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every module is an inverse limit of injectives


Author: George M. Bergman
Journal: Proc. Amer. Math. Soc. 141 (2013), 1177-1183
MSC (2010): Primary 16D50, 18A30; Secondary 13C11, 16D90
Published electronically: August 28, 2012
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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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Additional Information

George M. Bergman
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: gbergman@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11453-4
PII: S 0002-9939(2012)11453-4
Keywords: Inverse limit of injective modules
Received by editor(s): April 15, 2011
Received by editor(s) in revised form: August 16, 2011
Published electronically: August 28, 2012
Additional Notes: http://arXiv.org/abs/arXiv:1104.3173. After publication of this note, updates, errata, related references, etc., if found, will be recorded at http://math.berkeley.edu/˜gbergman/papers/.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.