TY - JOUR
T1 - Supertropical Monoids III
T2 - Factorization and splitting covers
AU - Izhakian, Zur
AU - Knebusch, Manfred
N1 - Publisher Copyright:
© World Scientific Publishing Company.
PY - 2024
Y1 - 2024
N2 - The category STROPm 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.
AB - The category STROPm 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.
KW - Monoids
KW - bipotent semirings
KW - lattices
KW - supertropical algebra
KW - supervaluations
KW - valuation theory
UR - http://www.scopus.com/inward/record.url?scp=85209394692&partnerID=8YFLogxK
U2 - 10.1142/S0219498826500155
DO - 10.1142/S0219498826500155
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AN - SCOPUS:85209394692
SN - 0219-4988
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
M1 - 2650015
ER -