Factorization in commutative rings and modules

This thesis with the title "Factorization in Commutative Rings and Modules" consists of six chapters. These chapters are introduction, unique factorization domains, unique factorization rings, unique factorization modules, the direct sum of unique factorization modules, results and discussion respectively. The first part is separated for the introduction. In the second and third part, some basic definitions and theorems are given necessary for thesis work. In the second part, the notion of unique factorization is studied over domain. In the third part, the notion of unique factorization is studied over commutative rings with zero divisor which are not domain. In the fourth part, the notion of unique factorization is studied over torsion free modules and then the notion is studied over non torsion free modules. Some properties in the rings have been worked over non torsion free modules. In the fifth part, especially, the direct sums of unique factorization modules are studied. The irreducible elements of some modules are examined. In the sixth part is separated for results and discussion.