TY  - JOUR
TT  - MODULES WITH FINITELY MANY SUBMODULES
AU  - Picavet, Gabriel
AU  - Picavet-l’hermitte, Martine
PY  - 2016
DA  - June
DO  - 10.24330/ieja.266197
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 119
EP  - 131
VL  - 19
IS  - 19
KW  - Idealization
KW  - ∆0-extension
KW  - SPIR
KW  - minimal ring extension
KW  - rami- fied
KW  - subintegral extension
KW  - FIP
KW  - FCP extension
KW  - Artinian ring
N2  - 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.
UR  - https://doi.org/10.24330/ieja.266197
L1  - http://dergipark.org.tr/en/download/article-file/232721
ER  -