THE VARIETY GENERATED BY AN AI-SEMIRING OF ORDER THREE
Xianzhong Zhao, Miaomiao Ren, Siniša Crvenković, Yong Shao, Petar Đapić
Abstract
Up to isomorphism, there are 61 ai-semirings of order three. The finite basis problem for these semirings is investigated. This problem for 45 semirings of them is answered by some results in the literature. The remaining semirings are studied using equational logic. It is shown that with the possible exception of the semiring \(S_7\), all ai-semirings of order three are finitely based.
Topics & Concepts
SemiringVariety (cybernetics)Isomorphism (crystallography)Order (exchange)MathematicsKleene algebraEquational logicBasis (linear algebra)Algebra over a fieldDiscrete mathematicsPure mathematicsComputer scienceProgramming languageFinanceEconomicsChemistryCrystallographyCrystal structureRewritingStatisticsGeometryEducational Technology and AssessmentFuzzy Logic and Control SystemsConstraint Satisfaction and Optimization