- Turkish Journal of Mathematics
- Vol: 41 Issue: 6
- Modules satisfying double chain condition on nonfinitely generated submodules have Krull dimension
Modules satisfying double chain condition on nonfinitely generated submodules have Krull dimension
Authors : Maryam Davoudian
Pages : 1570-1578
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Nonfinitely generated modules, Krull dimension, DICC-modules, n.f.g-DICC modules