Ural Mathematical Journal (Dec 2020)

THE VARIETY GENERATED BY AN AI-SEMIRING OF ORDER THREE

  • Xianzhong Zhao,
  • Miaomiao Ren,
  • Siniša Crvenković,
  • Yong Shao,
  • Petar Dapić

DOI
https://doi.org/10.15826/umj.2020.2.012
Journal volume & issue
Vol. 6, no. 2

Abstract

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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