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arXiv · 2404.06071

Subfitness in distributive (semi)lattices

Guram Bezhanishvili·James Madden·M. Andrew Moshier·Marcus Tressl·Joanne Walters-Wayland
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Abstract

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.

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Guram Bezhanishvili, James Madden, M. Andrew Moshier, Marcus Tressl, Joanne Walters-Wayland. 2025-03-25. Subfitness in distributive (semi)lattices. https://doi.org/10.1007/s00233-025-10506-5

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