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<p>We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 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, I

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Miaomiao Ren,
  • Junyang Liu,
  • Lingli Zeng,
  • Menglong Chen

摘要

We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 of them are finitely based and the remaining ones are nonfinitely based.