Abstract:
For a monounary algebra A = (A, f) we study
the lattice Quord A of all quasiorders of A, i.e., of all reflexive and
transitive relations compatible with f. Monounary algebras (A, f)
whose lattices of quasiorders are complemented were characterized
in 2011 as follows: (∗) f(x) is a cyclic element for all x ∈ A, and all
cycles have the same square-free number n of elements. Sufficiency
of the condition (∗) was proved by means of transfinite induction.
Now we will describe a construction of a complement to a given
quasiorder of (A, f) satisfying (∗).
