ABSTRACT
Let R be a commutative ring with identity. For a finitely generated R-module M, the notion of associated prime submodules of M is defined. It is shown that this notion inherits most of the essential properties of the usual notion of associated prime ideals. In particular, it is proven that for a Noetherian multiplication module M, the set of associated prime submodules of M coincides with the set of M-radicals of primary submodules of M which appear in a minimal primary decomposition of the zero submodule of M. Also, Anderson's (Citation1994) theorem is extended to minimal prime submodules in a certain type of modules.
Notes
Communicated by I. Swanson.