THE VARIETY GENERATED BY AN AI-SEMIRING OF ORDER THREE

Xianzhong Zhao     (Northwest University, Xi’an, 710069, P.R., China)
Miaomiao Ren     (Northwest University, Xi’an, 710069, P.R., China)
Siniša Crvenković     (University of Novi Sad, Novi Sad, 21102, Serbia)
Yong Shao     (Northwest University, Xi’an, 710069, P.R., China)
Petar Dapić     (University of Novi Sad, Novi Sad, 21102, Serbia)

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.


Keywords


Ai-semiring, Identity, Finitely based variety.

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References


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DOI: http://dx.doi.org/10.15826/umj.2020.2.012

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