THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE
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 factorizatio...
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Universitas Pattimura
2025-01-01
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| author | I Putu Yudi Prabhadika Sri Wahyuni |
| author_facet | I Putu Yudi Prabhadika Sri Wahyuni |
| author_sort | I Putu Yudi Prabhadika |
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| description | 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. |
| format | Article |
| id | doaj-art-eacb42f46ede4df6ac027d157f61b867 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-eacb42f46ede4df6ac027d157f61b8672025-08-20T04:01:48ZengUniversitas PattimuraBarekeng1978-72272615-30172025-01-0119141942610.30598/barekengvol19iss1pp419-42614036THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULEI Putu Yudi Prabhadika0Sri Wahyuni1Faculty of Vocational Studies, Universitas Warmadewa, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, IndonesiaT 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.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14036factorization domainunique factorization moduleweakly unique factorization module |
| spellingShingle | I Putu Yudi Prabhadika Sri Wahyuni THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE Barekeng factorization domain unique factorization module weakly unique factorization module |
| title | THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE |
| title_full | THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE |
| title_fullStr | THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE |
| title_full_unstemmed | THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE |
| title_short | THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE |
| title_sort | sufficient and necessary conditions for a module to be a weakly unique factorization module |
| topic | factorization domain unique factorization module weakly unique factorization module |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14036 |
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