Subfitness in Distributive (Semi)lattices

Authors

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

Document Type

Article

Publication Date

3-10-2025

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.

Comments

This article was originally published in Semigroup Forum in 2025. https://doi.org/10.1007/s00233-025-10506-5

Recommended Citation

Bezhanishvili, G., Madden, J., Moshier, M.A. et al. Subfitness in distributive (semi)lattices. Semigroup Forum (2025). https://doi.org/10.1007/s00233-025-10506-5

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.