Abstract
We introduce and study the c.Noetherian dimension of an module A, denoted by
which is the Noetherian dimension of the partially ordered set (briefly, poset) of countably generated submodules of A and prove that A has Noetherian dimension if and only if it has c.Noetherian dimension and furthermore
2020 Mathematics Subject Classification:
Acknowledgments
The author is deeply grateful to the referee for his/her meticulous reading and valuable suggestions which have definitely improved the paper.