Unities and Double Negation: Some Problems of Crapo and Le Conte de Poly-Barbut from ``Mathematical Essays in Honor of Gian-Carlo Rota"
by
Jonathan Farley
Vanderbilt University

Given a finite lattice L with unity of irreducibles I, the dual of L, L^*, is the completion of the negation of the unity I.

The finite lattices L that are isomorphic to their double-duals (L^**) are characterized. It is shown that L^** need not be embeddable in L; indeed, L^** need not even be in the variety generated by L.

The problems in Crapo and Le Conte de Poly-Barbut's paper from Mathematical Essays in Honor of Gian-Carlo Rota are thus solved.

http://www.math.vanderbilt.edu/faculty/Farley.html

Date received: May 23, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafg-18.