Factorization of Modules on Commutative Rings

In this article, the factorization of a torsion module structure is examined and definitions and theorems related to the uniform factorization part in modules are given. Then, the prime sub-modules of the modules that can be factorized by a single method are examined and basic definitions and theorems are given. We have also studied the module elements in written form as the product of the unreducible elements of the ring with the unreducible elements of the modules with the help of weak prime units defined on the torsion modules.