Turkish Journal of Mathematics
Abstract
We prove the result in the title. We study submodules $N$ of a module $M$ such that whenever $\frac{M}{N}$ satisfies the double infinite chain condition so does $M$.Moreover, we observe that an $\alpha $-atomic module, where $\alpha\geq 2$ is an ordinal number, satisfies the previous chain if and only if it satisfies the descending chain condition on nonfinitely generated submodules.
DOI
10.3906/mat-1501-14
Keywords
Nonfinitely generated modules, Krull dimension, DICC-modules, n.f.g-DICC modules
First Page
1570
Last Page
1578
Recommended Citation
DAVOUDIAN, M (2017). Modules satisfying double chain condition on nonfinitely generated submodules have Krull dimension. Turkish Journal of Mathematics 41 (6): 1570-1578. https://doi.org/10.3906/mat-1501-14
