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<p>We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope.</p>

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Subfitness in distributive (semi)lattices

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月10日

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  • G. Bezhanishvili,
  • J. Madden,
  • M. A. Moshier,
  • M. Tressl,
  • J. Walters-Wayland

摘要

We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope.