Modules With Chain Conditions On δ -Small Submodules - Hasan, Wasan (Iraqi Journal of Science, 2023)
Let R be an associative ring with identity and M be unital non zero R-module. Asubmodule N of a module M is called a δ-small submodule of M (briefly N << M )ifN+X=M for any proper submodule X of M with M/X singular, we haveX=M .In this work,we study the modules which satisfies the ascending chain condition(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Thenwe generalize this conditions into the rings , in the last section we get same resultson δ- supplement submodules and we discuss some of these results on this types ofsubmodules.