Generic extensions and multiplicative bases of quantum groups at ${{\mathbf q=0}}$

We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at $q=0$ of Ringel's Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig's canonical basis.