Supertropical Monoids III: Factorization and splitting covers

2024/08/20 by Zur Izhakian, Izhakian, Zur, Manfred Knebusch +1 · 1 citation
Computer Science · Mathematics · #06B23 #12K10 #13F30 #14T05 #16W60 #16Y60 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13A18 #Rings, Modules, and Algebras #Secondary: 03G10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2408.10772

openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Factorization in Finitely-Presented Monoids

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