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<p>We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are 112 such algebras. We show that 106 of them are finitely based and the remaining ones are nonfinitely based.</p>

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The finite basis problem for additively idempotent semirings of order four, III

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Miaomiao Ren,
  • Zexi Liu,
  • Mengya Yue,
  • Yizhi Chen

摘要

We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are 112 such algebras. We show that 106 of them are finitely based and the remaining ones are nonfinitely based.