Four notes on quasiorder lattices
Ivan Chajda, Gábor Czédli · Czech digital mathematics library · 1996
The quasiorders, i.e., reflexive, transitive and compatible relations, of a (partial) algebra A form a lattice Quord(A) with an involution p \-> p~ l = {(x,_y) : (y,x) E p} .It is shown that every algebraic lattice with involution is isomorphic to Quord(A) for some partial algebra A. Any finite distributive lattice with involution is isomorphic to Quord(A) for some finite algebra A such that the quasiorders of A are 3-permutable.Every distributive lattice with involution can be embedded in Quord(A) for some set A. Any algebraic lattice is isomorphic to Quord(A) for some algebra A such that Quord(A) = Con(A).