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<p>We describe varieties of commutative semigroups in which free countable semigroups embed into finitely generated commutative semigroups. We also refute two natural embeddability conjectures; in particular, we show that the finiteness of the number of Archimedean components is not necessary for the embeddability into finitely generated commutative semigroups. We establish a criterion for the embeddability of cancellative semigroups into finitely generated commutative semigroups.</p>

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On the embedding of semigroups into finitely generated commutative semigroups

  • 期刊论文

  • 发表日期：

    2025年4月11日

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  • Stanislav I. Kublanovsky

摘要

We describe varieties of commutative semigroups in which free countable semigroups embed into finitely generated commutative semigroups. We also refute two natural embeddability conjectures; in particular, we show that the finiteness of the number of Archimedean components is not necessary for the embeddability into finitely generated commutative semigroups. We establish a criterion for the embeddability of cancellative semigroups into finitely generated commutative semigroups.