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Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE

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  • I Putu Yudi Prabhadika,
  • Sri Wahyuni
I Putu Yudi Prabhadika
Faculty of Vocational Studies, Universitas Warmadewa, Indonesia
Sri Wahyuni
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss1pp419-426
Published January 13, 2025
Keywords
  • Factorization Domain,
  • Unique Factorization Module,
  • Weakly Unique Factorization Module
How to Cite
[1]
I. P. Y. Prabhadika and S. Wahyuni, “THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 419-426, Jan. 2025.

Copyright (c) 2025 I Putu Yudi Prabhadika, Sri Wahyuni

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.

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