Remark on partially ordered sets, universal algebras and semigroups
Robert Šulka · Czech digital mathematics library · 1979
In the paper left segments of a partially ordered set P and some subsystems of the system of all left segments of P are studied.Results are applied by studying the system of subalgebras of a B -algebra (see Def. 3.), especially by studying the system of subalgebras of unary algebras and B-semigroups and by studying systems of ideals of semigroups.Some results of papers [1, 2, 3, 7, 9 and 10] are generalized and completed.The possibility of solving the above problems is given by Theorem 15, since by this Theorem the partially ordered set of all subalgebras of a B -algebra is isomorphic to the partially ordered system of all left segments of the partially ordered set of all ^-equivalence classes (see the beginning of section 2) of this B -algebra.