DISTRIBUTIVE MODULES AND PRIME DIVISORS

Let R be a commutative ring with identity and let M be an R-module. In this paper we prove that M is distributive if and only if the set of all weakly p-primal subsets of M is linearly ordered, and, if and only if each submodule of M can be reoresented as an intersection of irreducible isolated components. Some other equivalent conditions for M to be distributive will be investigated.

Keywords:

distributive modules , associated primes