Lucia Janičková – Congruence lattices of connected monounary algebras

Pavol Jozef Šafárik University in Košice

The system of all congruences of an algebra (A,F) forms a lattice, denoted Con(A,F). Further, the system of all congruence lattices of all algebras with the base set A forms a lattice $E_A$

. We deal with meet-irreducibility in $E_A$

for a given finite set A. All meet-irreducible elements of $E_A$

are congruence lattices of monounary algebras. Some types of meet-irreducible congruence lattices were already described. In the case when a monounary algebra (A, f) is connected, we prove necessary and sufficient condition under which Con(A,f) is meet-irreducible