Associated Prime Submodules of Finitely Generated Modules

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 (1994) theorem is extended to minimal prime submodules in a certain type of modules.

Key Words:

• Associated prime ideals
• Prime submodules
• Quasi multiplication modules

2000 Mathematics Subject Classification:

• 13E05
• 13E10
• 13C99

Notes

Communicated by I. Swanson.