The lattice of projection operators of a subtractibe nearsemilattice
by
Jānis Cīrulis
Depatment of Computer Science, University of Latvia, Riga, Latvia

A nearsemilattice is a poset in which every principal order ideal is a join semilattice. A nearsemilattice A is subtractive if it has the least element 0 and is equipped with a total binary operation - satisfying the following axioms:

(i) if y \/ z exists, then x - y <= z iff x <= y \/ z,
(ii) if x - y <= z, then x - z <= y.

A projection operator on A is an idempotent endomorphism f such that f(x) <= x. We characterize the kernel ideals f ^-1(0) of projection operators and prove that these operators form, under the pointwise ordering, a bounded lattice which is dually embeddable in the (distributive) lattice of ideals of A.

Reference
[1] Cirulis J. Subtractive nearsemilattices. Proc. Latvian Acad. Sci. 52B (1998), 228-233.

Date received: June 13, 2002

Copyright © 2002 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 # caiv-24.