Skip Navigation


Journal of the London Mathematical Society Advance Access originally published online on November 19, 2007
Journal of the London Mathematical Society 2007 76(3):797-811; doi:10.1112/jlms/jdm076
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
76/3/797    most recent
jdm076v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Guil Asensio, P. A.
Right arrow Articles by Herzog, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

Indecomposable flat cotorsion modules

Pedro A. Guil Asensio

Departamento de Matemáticas
Universidad de Murcia
30100 Espinardo
Murcia
Spain

Ivo Herzog

The Ohio State University at Lima
Lima
OH 45804
USA
herzog.23{at}osu.edu

An additive functor from the category of flat right R-modules to the category of abelian groups is continuous if it is isomorphic to a functor of the form–{otimes}R M, where M is a left R-module. It is shown that for any simple subfunctor A of–{otimes} M there is a unique indecomposable flat cotorsion module UR for which A(U)!=0. It is also proved that every subfunctor of a continuous functor contains a simple subfunctor. This implies that every flat right R-module may be purely embedded into a product of indecomposable flat cotorsion modules.

If CE(R) is the cotorsion envelope of RR and S= End;R CE(R), then a local ring monomorphism is constructed from R/J(R) to S/J(S). This local morphism of rings is used to associate a semiperfect ring to any semilocal ring. It also proved that if R is a semilocal ring and M a simple left R-module, then the functor–{otimes}R M on the category of flat right R-modules is uniform, and therefore contains a unique simple subfunctor.

2000 Mathematics Subject Classification 03C60, 03C98, 16D40, 15D50, 16D90, 16E30, 16L30, 16P70, 18A30.

The first author is partially supported by the DGI (BFM 2000-0346, Spain) and by the Fundaci'on S'eneca (PI-76/00515/FS/01). The second author is partially supported by NSF grants DMS-02-00698 and DMS-05-01207.

Received October 10, 2005; published online November 19, 2007.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.