Posets and meet-irreducibles
by
Branimir Seselja
Institute of Mathematics, University of Novi Sad
Coauthors: Andreja Tepavcevic

Every compactly generated poset is, up to the isomorphism, a particular subposet of the distributive algebraic lattice with the same poset of completely meet-irreducible elements.

In the presence of some additional finiteness condition, the collection of all such partially ordered sets with the same poset of meet-irreducibles can be ordered into a complete and atomic Boolean lattice. Join-semilattices from this collection form a lattice, while lattices generally do not. However, if there is the smallest lattice in the collection, then these also form a lattice under inclusion. Some representations of lattices by the above collections are given.

Date received: April 9, 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 # caee-18.