In abstract algebra, a branch of mathematics, a maximal semilattice quotient is a commutative monoid derived from another commutative monoid by making certain elements equivalent to each other. Every commutative monoid can be endowed with its algebraic preordering ≤ . By definition, x≤ y holds, if there exists z such that x+z=y. Further, for x, y in M, let hold, if there exists a positive integer n such that x≤ ny, and let hold, if and . The binary relation is a monoid congruence of M, and the quotient monoid is the maximal semilattice quotient of M.
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