On retract lattices of monounary algebras
by
Jozef Pócs
Mathematical Institute, Slovak Academy of Sciences, Košice
Coauthors: Danica Jakubíková-Studenovská, Faculty of Science, P.J. Šafárik University, Košice

By a retract we understand any image of an idempotent endomorphism. The system of all retracts of a given monounary algebra forms an upper semilattice. If this system contains the least element then it forms a complete lattice. We investigate the system of all retracts endowed by the empty set and also we investigate monounary algebras with the least retract. We show that the lattice of retracts of a monounary algebra is semimodular and we give a description of all monounary algebras with a complemented lattice of retracts. In particular, the lattice of retracts of a monounary algebra is complemented if and only if it is boolean. Further, we deal with the existence of a diamond in the retract lattice of a monounary algebra.

Date received: May 15, 2007

Copyright © 2007 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 # catx-45.