Supertropical Monoids III: Factorization and splitting covers
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arXiv
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| Format: | Preprint |
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2024
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| author | Izhakian, Zur Knebusch, Manfred |
| author_facet | Izhakian, Zur Knebusch, Manfred |
| contents | The category $STROP_m$ of supertropical monoids, whose morphisms are transmissions, has the full--reflective subcategory $STROP$ of commutative semirings. In this setup, quotients are determined directly by equivalence relations, as ideals are not applicable for monoids, leading to a new approach to factorization theory. To this end, tangible factorization into irreducibles is obtained through fiber contractions and their hierarchy. Fiber contractions also provide different quotient structures, associated with covers and types of splitting covers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_10772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supertropical Monoids III: Factorization and splitting covers Izhakian, Zur Knebusch, Manfred Commutative Algebra Primary: 13A18, 13F30, 16W60, 16Y60, Secondary: 03G10, 06B23, 12K10, 14T05 The category $STROP_m$ of supertropical monoids, whose morphisms are transmissions, has the full--reflective subcategory $STROP$ of commutative semirings. In this setup, quotients are determined directly by equivalence relations, as ideals are not applicable for monoids, leading to a new approach to factorization theory. To this end, tangible factorization into irreducibles is obtained through fiber contractions and their hierarchy. Fiber contractions also provide different quotient structures, associated with covers and types of splitting covers. |
| title | Supertropical Monoids III: Factorization and splitting covers |
| topic | Commutative Algebra Primary: 13A18, 13F30, 16W60, 16Y60, Secondary: 03G10, 06B23, 12K10, 14T05 |
| url | https://arxiv.org/abs/2408.10772 |