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.