ITERATIVE SEPARATION IN DISTRIBUTIVE CONGRUENCE LATTICES

In [PLOSCICA, M.: Separation in distributive congruence lattices, Algebra Universalis 49 ( 2003), 1-12] we defined separable sets in algebraic lattices and showed a close connection between the types of non-separable sets in congruence lattices of algebras in a finitely generated congruence distributive variety V and the structure of subdirectly irreducible algebras in V. Now we generalize these results using the concept of separable mappings ( defined on some trees) and apply them to some lattice varieties. (C) 2009 Mathematical Institute Slovak Academy of Sciences