A note on regular congruences of ordered semigroups

摘要

In this note we first extend Theorem 4.2 from Xiang-Yun (Semigroup Forum 61:159-178, 2000) by showing that the set of all regular congruences with the ordering is actually an algebraic lattice. Afterwards, we derive Maltsev type description of principal regular congruences. Lastly, we rectify an error in Example 4.7 from Xiang-Yun 2000.