| Abstrak/Abstract |
A torsion-free module over an integral domain is called Unique Factorization Module
(UFM) if satisfied some conditions: (1) Every non-zero element ∈ has an irreducible
factorization, that is …
, with , ,…,
are irreducible in and is
irreducible in , and (2) if …
…
are two irreducible
factorizations of , then , ~ in , and we can rearrange the order of the
’s so
that ~
in for every ∈ 1, 2,…, . The definition of UFM is a generalization of the
concept of factorization on the ring which is applied to the module. In this study, we will
discuss another definition that is a generalization of UFM, namely by the Weakly Unique
Factorization Module (w-UFM). First, some concepts that play an important role in defining
w-UFM are given. After that, the definition and characterization of w-UFM is also given.
The results of this study will provide the sufficient and necessary conditions of the w-UFM. |
