(untitled) (JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences, 2020)
We introduce modules with finite spanning isodimension. Let be an module is called module with finite spanning isodimension, if for every strictly decreasing sequence, there exists a positive integer such that is isosmall for each . In the following sense, we define isosmall submodule, a submodule of an module is called isosmall, if , then for any submodule of . Some other classes are studied for instances isomaximal and many results are proved. On the other hand, we determine that the ring of endomorphisms of an isosimple module is a local ring.