Factorization of Modules on Commutative Rings
Ali Karakuş
*
Department of Mathematics, Faculty of Science, Kilis 7 Aralık University, Kilis, Türkiye.
Merve Gökçe
Department of Mathematics, Faculty of Science, Kilis 7 Aralık University, Kilis, Türkiye.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Torsion module, factorization of module, weak prime module