On Modules with Finite Spanning Isodimension

Abstract

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.