User:KBlott:Questions\Is the set of protointegers a semilattice with respect to meet?

$(\mathbb N \times \mathbb N, \wedge)$ is a semigroup. $(\mathbb N \times \mathbb N, \wedge)$ is abelian since $max(x,y) = max(y,x)$. $(\mathbb N \times \mathbb N, \wedge)$ is idempotent since $max(x,x) = x$. Therefore, $(\mathbb N \times \mathbb N, \wedge)$ is a semilattice.