The varieties of semilattice-ordered semigroups satisfying x(3) approximate to x and xy approximate to yx

摘要

The aim of this paper is to study the varieties of semilattice-ordered Burnside semigroups satisfying x(3) approximate to x and xy approximate to yx. It is shown that the collection of all such varieties forms a distributive lattice of order 9. Also, all of them are finitely based and finitely generated. This gives a generalization and expansion of the results obtained by McKenzie and Romanowska (Contrib Gen Algebra Proc Klagenf Conf 1978 1:213-218, 1979).