Title of article :
The small condition for modules with Noetherian dimension
Author/Authors :
Shirali ، Nasrin Department of Mathematics - Shahid Chamran University of Ahvaz , Kavoosi Ghafi ، Hooriya Department of Mathematics - Shahid Chamran University of Ahvaz , Javdannezhad ، Malek Department of Mathematics - Shahid Rajaee Teacher Training University
Abstract :
A module M with Noetherian dimension is said to satisfy the small condition, if for any small submodule S of M the Noetherian dimension of S is strictly less than the Noetherian dimension of M. For an Artinian module M, this is equivalent to that M is semisimple. In this article, we introduce and study this concept and observe some basic facts for modules with this condition.
Keywords :
Large condition , Small condition , Semiatomic modules , Projective cover
Journal title :
Journal of Mahani Mathematical Research Center
Journal title :
Journal of Mahani Mathematical Research Center
