LATTICE OF QUASIORDERS OF MONOUNARY ALGEBRAS.

For an algebra A, the lattice Quord A of all quasiorders of A, i. e., of all reflexive and transitive relations compatible with all fundamental operations of A, is dealt with. In the present paper we prove that if A is a monounary algebra, then Quord A is distributive if and only if it is modular and we find necessary and sufficient conditions for A under which Quord A is distributive. [ABSTRACT FROM AUTHOR]