NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS

In this paper, we introduce a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring with identity, and M be an R-module such that Nil(M) is a divided prime submodule of M. M is called a nonnil-Noetherian R-module if every nonnil submodule of M is nitely-generated. We prove that many properties of the Noether- ian modules are also true for the nonnil-Noetherian modules.