On some admissible lattices

Abstract

This paper explores applications of the so-called Freese's technique, a classical approach to study the congruence variety of a given algebra. We leverage this tool to investigate lattices that are admissible as congruence sublattice of a given algebra. In particular, we present a novel characterization of congruence modular varieties, Taylor varieties, and varieties satisfying a non-trivial congruence identity by means of lattice omission.