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The category Formula: see text of supertropical monoids, whose morphisms are transmissions, has the full-reflective subcategory Formula: see text 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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Izhakian et al. (Fri,) studied this question.
www.synapsesocial.com/papers/68e5b3b6b6db64358754c877 — DOI: https://doi.org/10.1142/s0219498826500155
Zur Izhakian
Manfred Knebusch
Journal of Algebra and Its Applications
University of Regensburg
Ariel University
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