On modules with finite spanning isodimension

الملخص EN

We introduce ? −modules with finite spanning isodimension.

let ? be an ? −module ? is called module with finite spanning isodimension, if for every strictly decreasing sequence ?0 ⊇ ?1 ⊇ ⋯, 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.