Equational theories of idempotent semifields

2024/02/15 by George Metcalfe, Metcalfe, George, Simon Santschi +1
Decision Sciences · #03C05 #06F15 #12K10 #16Y60 #FOS: Mathematics #Logic (math.LO) #Scheduling and Timetabling Solutions

paper · pdf · doi:10.48550/arxiv.2402.09876

openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii) there are continuum-many equational theories of classes of idempotent semifields; and (iii) the equational theory of the class of idempotent semifields is co-NP-complete.

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