Abstract—We study commutative idempotent semirings in general, and some examples in particular. We show that the class Red of semiring reducts of MV-algebras, although axiomatized by a first order theory, is not axiomatized by a geometric theory (in the topos-theoretic sense) or a universal-existential first order theory. Then we perform comparisons between the class Red, the class of all semirings, and some so-called exotic semirings.

On semirings and MV-algebras

DI NOLA, Antonio;LENZI, Giacomo
2017

Abstract

Abstract—We study commutative idempotent semirings in general, and some examples in particular. We show that the class Red of semiring reducts of MV-algebras, although axiomatized by a first order theory, is not axiomatized by a geometric theory (in the topos-theoretic sense) or a universal-existential first order theory. Then we perform comparisons between the class Red, the class of all semirings, and some so-called exotic semirings.
978-1-5090-6034-4
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4688563
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