Indecomposable flat cotorsion modules |
| |
Authors: | Guil Asensio, Pedro A. Herzog, Ivo |
| |
Affiliation: | Departamento de Matemáticas Universidad de Murcia 30100 Espinardo Murcia Spain |
| |
Abstract: | An additive functor from the category of flat right R-modulesto the category of abelian groups is continuous if it is isomorphicto a functor of the form–R M, where M is a left R-module.It is shown that for any simple subfunctor A of– M thereis a unique indecomposable flat cotorsion module UR for whichA(U)0. It is also proved that every subfunctor of a continuousfunctor contains a simple subfunctor. This implies that everyflat right R-module may be purely embedded into a product ofindecomposable 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) toS/J(S). This local morphism of rings is used to associate asemiperfect ring to any semilocal ring. It also proved thatif R is a semilocal ring and M a simple left R-module, thenthe functor–R M on the category of flat right R-modulesis uniform, and therefore contains a unique simple subfunctor. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|