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<p>We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts have the least element and two coatoms. Up to isomorphism, there are 93 such algebras. We show that with the exception of the semiring <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_908_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_{(4, 435)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mo>,</mo> <mn>435</mn> <mo stretchy="false">)</mo> </mrow> </msub> </math></EquationSource> </InlineEquation>, all of them are finitely based.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Meng Ya Yue,
  • Miao Miao Ren,
  • Ling Li Zeng,
  • Yong Shao

摘要

We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts have the least element and two coatoms. Up to isomorphism, there are 93 such algebras. We show that with the exception of the semiring \(S_{(4, 435)}\) S ( 4 , 435 ) , all of them are finitely based.