  We adapt the construction of the Grothendieck group associated to a
commutative mono\"id to handle idempotent mono\"ids. Our construction works for
a restricted class of commutative mono\"ids, it agrees with the Grothendieck
group construction in many cases and yields a hypergroup which solves the
universal problem for morphisms to hypergroups. It gives the expected
non-trivial hypergroup construction in the case of idempotent mono\"ids.
