  P.J.Cameron introduced the orbit algebra of a permutation group and
conjectured that this algebra is an integral domain if and only if the group
has no finite orbit. We prove that this conjecture holds and in fact that the
age algebra of a relational structure $R$ is an integral domain if and only if
$R$ is age-inexhaustible. We deduce these results from a combinatorial lemma
asserting that if a product of two non-zero elements of a set algebra is zero
then there is a finite common tranversal of their supports. The proof is built
on Ramsey theorem and the integrity of a shuffle algebra.
