Coregularity of endomorphism monoids of unars
Direct limits of monounary algebras
Directable automata and their generalizations: A survey.
Distinguishing subsets in general algebras
DR-irreducibility of connected monounary algebras
DR-irreducibility of connected monounary algebras with a cycle
Endomorphisms and connected components of partial monounary algebras
Endomorphisms of partial monounary algebras
Equation for given real functions ,
We investigate functional equations where and are given real functions defined on the set of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions which are strictly increasing and continuous on . In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present a construction...
Equational bases for weak monounary varieties
It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
Existence of monomorphisms of partial unary algebras
Families of independent sets in finite unary algebras
Globals of unary algebras
Graph homomorphisms of partial monounary algebras
Homogeneous monounary algebras
Homomorphic images of finite subdirectly irreducible unary algebras
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.
Homomorphisms and strong homomorphisms of relational structures
Homomorphisms of algebras
A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra...
Homomorphisms of machines. I
Homomorphisms of machines. II