On regular anti-congruence in anti-ordered semigroups
Abraham Romano · Publications de l Institut Mathematique · 2007
For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, _=, ?, ?) ordered under anti-order ? if there exists an antiorder ? on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder ? on S under ? such that q = ? ? ??1. Besides, for regular anti-congruence q on S, a construction of the maximal quasi-antiorder relation under ? with respect to q is shown.