Subfitness in distributive (semi)lattices

Authors

G. Bezhanishvili, New Mexico State University
J. Madden, Louisiana State University
M. A. Moshier, Chapman University
M. Tressl, The University of Manchester
J. Walters-Wayland, Chapman University

Document Type

Article

Publication Date

6-1-2025

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.

Publication Source (Journal or Book title)

Semigroup Forum

First Page

511

Last Page

524

Recommended Citation

Bezhanishvili, G., Madden, J., Moshier, M., Tressl, M., & Walters-Wayland, J. (2025). Subfitness in distributive (semi)lattices. Semigroup Forum, 110 (3), 511-524. https://doi.org/10.1007/s00233-025-10506-5