Cardinal arithmetic of a certain class of monounary algebras
Cardinalities of lattices of topologies of unars and some related topics
In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
Cardinality of retracts of monounary algebras
For an uncountable monounary algebra with cardinality it is proved that has exactly retracts. The case when is countable is also dealt with.
Characterizations of certain general and reproductive solutions of arbitrary equations
Characterizations of certain monounary algebras. I
Characterizations of certain monounary algebras. II
Church-Rosser property and decidability of monadic theories of unary algebras
Congruence lattices of intransitive G-Sets and flat M-Sets
An M-Set is a unary algebra whose set of operations is a monoid of transformations of ; is a G-Set if is a group. A lattice is said to be represented by an M-Set if the congruence lattice of is isomorphic to . Given an algebraic lattice , an invariant is introduced here. provides substantial information about properties common to all representations of by intransitive G-Sets. is a sublattice of (possibly isomorphic to the trivial lattice), a -product lattice. A -product...
Construction of all homomorphisms of groupoids
Construction of all homomorphisms of mono--ary algebras
Construction of all strong homomorphisms of binary structures
Convex automorphisms of partial monounary algebras
Convex subsets of partial monounary algebras
Coregularity of endomorphism monoids of unars