Journals / International Electronic Journal of Algebra / 2020 / Cilt: 28 - Sayı: 28
AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES
- Pages
- 229–229
- DOI
- —
Abstract
Abstract of the paper: "G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.":We characterize ring extensions $R \subset S$ 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. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$