AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES

Authors : Gabriel PICAVET, Martine PICAVETL`HERMITTE

Pages : 229-229

Doi:10.24330/ieja.768272

View : 12 | Download : 14

Publication Date : 2020-07-14

Article Type : Other Papers

Abstract :Abstract of the paper: `G. Picavet and M. Picavet-L`Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 insert ignore into journalissuearticles values(2016);, 119-131.`: We characterize ring extensions $R \subset S$ 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, minimal ring extension, subintegral extension