Subfitness in distributive (semi)lattices
arXiv:2404.06071 · doi:10.1007/s00233-025-10506-5
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.
Final Version (14 pages)