On Prime Submodules of a Finitely Generated Free Module Over a Commutative Ring

Abstract

In this article, we give a full characterization of prime submodules of a finitely generated free module F over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of F and characterize the minimal primary decomposition of this submodule. We also describe the structure of prime submodules of a module over a Dedekind domain.

Key Words:

• Dedekind domain
• Prime submodule
• Primary decomposition
• Primary submodule

2010 Mathematics Subject Classification:

• 13A99
• 13C10
• 13C99
• 13F05

ACKNOWLEDGMENT

The authors would like to thank the referee for his/her useful suggestions that improved the presentation of this article.