Quasiorders of lattices versus pairs of congruences. (English) Zbl 0829.06008

Czédli, Gábor; Szabó, László

Acta Sci. Math. 60, No. 1-2, 207-211 (1995).

Summary: Given a lattice \(L\), the lattice, in fact the involution lattice, \(\text{Quord} (L)\) of quasiorders of \(L\) is shown to be isomorphic with \(\text{Con}^2 (L)\), the direct square of the congruence lattice of \(L\). The isomorphism given is natural in category-theoretic sense. As a corollary, a description of compatible partial orderings of a lattice is obtained.

MSC:

06B05	Structure theory of lattices
06B10	Lattice ideals, congruence relations
08A30	Subalgebras, congruence relations

Keywords:

lattice of quasiorders; category; involution lattice; congruence lattice; isomorphism; compatible partial orderings of a lattice