Length-Factoriality and Pure Irreducibility
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916167461896192 |
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| author | Bu, Alan Vulakh, Joseph Zhao, Alex |
| author_facet | Bu, Alan Vulakh, Joseph Zhao, Alex |
| contents | An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The notion of length-factoriality was introduced by J. Coykendall and W. Smith in 2011 under the term 'other-half-factoriality': they used length-factoriality to provide a characterization of unique factorization domains. In this paper, we study length-factoriality in the more general context of commutative, cancellative monoids. In addition, we study factorization properties related to length-factoriality, namely, the PLS property (recently introduced by Chapman et al.) and bi-length-factoriality in the context of semirings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_06638 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Length-Factoriality and Pure Irreducibility Bu, Alan Vulakh, Joseph Zhao, Alex Commutative Algebra Primary: 13F15, 13A05, Secondary: 16Y60 An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The notion of length-factoriality was introduced by J. Coykendall and W. Smith in 2011 under the term 'other-half-factoriality': they used length-factoriality to provide a characterization of unique factorization domains. In this paper, we study length-factoriality in the more general context of commutative, cancellative monoids. In addition, we study factorization properties related to length-factoriality, namely, the PLS property (recently introduced by Chapman et al.) and bi-length-factoriality in the context of semirings. |
| title | Length-Factoriality and Pure Irreducibility |
| topic | Commutative Algebra Primary: 13F15, 13A05, Secondary: 16Y60 |
| url | https://arxiv.org/abs/2210.06638 |