MODULES WITH FINITELY MANY SUBMODULES

Year 2016, Volume: 19 Issue: 19, 119 - 131, 01.06.2016

Gabriel Picavet Martine Picavet-l’hermitte

https://doi.org/10.24330/ieja.266197

Cited By: 11

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