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, MARYAM
(2017)
"Modules satisfying double chain condition on nonfinitely generated submodules have Krull dimension,"
Turkish Journal of Mathematics: Vol. 41:
No.
6, Article 16.
https://doi.org/10.3906/mat-1501-14
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss6/16
