Title of article :
MODULES WITH FINITELY MANY SUBMODULES
Author/Authors :
Picavet, Gabriel Universite Blaise Pascal - Laboratoire de Math´ematiques UMR 6620 CNRS - Les C´ezeaux, 24 Avenue des Landais, France , Picavet-L’Hermitte, Martine Universite Blaise Pascal - Laboratoire de Math´ematiques UMR 6620 CNRS - Les C´ezeaux, 24 Avenue des Landais, France
Abstract :
We characterize ring extensions R ⊂ S having FCP (FIP), where
S is the idealization of some R-module. As a by-product we exhibit characterizations of the modules that have finitely many submodules. Our tools
are minimal ring morphisms, while Artinian conditions on rings are ubiquitous
Keywords :
Idealization , ∆0-extension , SPIR , minimal ring extension , rami fied , subintegral extension , FIP , FCP extension , Artinian ring
Journal title :
International Electronic Journal of Algebra
