Abstract
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 $$\subseteq $$ 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.
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