Homomorphisms of unary algebras and of their expansions
In this paper the notion of an interval in a partial monounary algebra is introduced and pairs , of partial monounary algebras are investigated such that each interval in is also an interval in , and conversely.
In this paper we describe all algebras with one unary operation such that by a direct limit construction exactly two nonisomorphic algebras can be obtained from .
Fraïssé introduced the notion of a -set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: , , —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and , , —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.
In this paper we investigate the validity of a cancellation law for some classes of monounary algebras.
In this note we deal with a question concerning monounary algebras which is analogous to an open problem for partially ordered sets proposed by Duffus and Rival.