MODULES WITH FINITELY MANY SUBMODULES

Authors : Gabriel Picavet, Martine PicavetL’Hermitte

Pages : 119-131

Doi:10.24330/ieja.266197

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Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :We characterize ring extensions R ⊂ S having FCP insert ignore into journalissuearticles values(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