 By definition, "x≤ y" holds, if there exists "z" such that "x+z=y".Further, for "x, y" in "M", let formula_1 hold, if there exists a positive integer "n" such that "x≤ ny", and let formula_2 hold, if formula_1 and formula_4.The binary relation formula_5 is a monoid congruence of "M", and the quotient monoid formula_6 is the "maximal semilattice quotient" of "M".