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arXiv · 2508.01212

The finite basis problem for the endomorphism semirings of finite semilattices

Igor Dolinka·Sergey V. Gusev·Mikhail V. Volkov
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Abstract

For every semilattice $\mathcal{A}=(A,+)$, the set $\mathrm{End}(\mathcal{A})$ of its endomorphisms forms a semiring under pointwise addition and composition. We prove that that if $\mathcal{A}$ is finite, then the endomorphism semiring $\mathrm{End}(\mathcal{A})$ has a finite identity basis if and only if $|A|\le 2$.

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Igor Dolinka, Sergey V. Gusev, Mikhail V. Volkov. 2025-08-02. The finite basis problem for the endomorphism semirings of finite semilattices. https://doi.org/10.36045/j.bbms.250801

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