The Sufficient and Necessary Conditions for a Module to Be a Weakly Unique Factorization Module
Year: 2025
Type: article
Abstract: T 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 . 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.
Authors: I Putu Yudi Prabhadika, Sri Wahyuni
Institutions: Warmadewa University, Universitas Gadjah Mada
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Universitas Gadjah Mada
OpenAlex ID: W4406337695