Lattices of quasiorders on universal algebras
Ivan Chajda, A. G. Pinus, A. J. Denisov · Czechoslovak Mathematical Journal · 1999
Lattices of quasiorders were studied mainly by G. Czédli and A. Lenkehegyi [2] and by A. G. Pinus and I. Chajda [9].These investigations were done both for universal algebras and algebras of special sorts: lattices, semilattices etc.In some cases, the lattice of all quasiorders of an algebra A has similar properties as the congruence lattice Con A , however, there are also essential distinctions.One of the traditional questions concerning congruence lattices is a characterization of congruence lattices satisfying given identities.It was partly solved for quasiorder lattices and for varieties of algebras in [2], [8], [9].An abstract algebraic characterization of quasiorder lattices was settled in [1], [8].The aim of this paper is to characterize concrete quasiorder lattices and to represent these lattices by quasiorder lattices of algebras of restricted similarity types.