Some results on prime and primary submodules

Abstract

This article is devoted to study some properties of prime and primary submodules. First we characterize prime submodules of free modules and give a primality condition for certain submodules in terms of associated prime ideals. Furthermore, by using symmetric algebra of modules we describe Rees algebras associated to prime submodules and provide a computational method to check if some primary submodules of a free module have prime radical.