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Antiatomic retract varieties of monounary algebras
by
Danica Jakubíová-Studenovská
Dept. of Geom. and Algebra, Safárik University, Jesenná 5, Kosice, SK--041 54, Slovakia
A class of algebras of a given type is called a retract variety if it is product closed and retract closed. A retract variety V is atomic if V is nonempty and whenever U is nonempty retract variety which is a subclass of V, then U=V. A nonempty retract variety V is said to be antiatomic if there is no atomic variety V1 such that V1 is a subclass of V. Let At (Ant) be the system of all atomic (antiatomic) monounary algebras. We describe all members of At and Ant, respectively. The system At contains (up to isomorphism) exactly 2\aleph0 elements. Next, Ant is closed under inf and sup and there is a chain (antichain) in Ant which is a proper class.
Date received: November 30, 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 # cafo-23.