Abstract
The system of all congruences of an algebra (A, F) forms a lattice, denoted $${{\,\mathrm{Con}\,}}(A, F)$$ . Further, the system of all congruence lattices of all algebras with the base set A forms a lattice $$\mathcal {E}_A$$ . We deal with meet-irreducibility in $$\mathcal {E}_A$$ for a given finite set A. All meet-irreducible elements of $$\mathcal {E}_A$$ 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 $${{\,\mathrm{Con}\,}}(A, f)$$ is $$\wedge $$ -irreducible.
Published Version
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