  Let P a locally finite partially ordered set, F a field, G a group, and
I(P,F) the incidence algebra of P over F. We describe all the inequivalent
elementary G-gradings on this algebra. If P is bounded, F is a infinite field
of characteristic zero, and A, B are both elementary G-graded incidence
algebras satisfying the same G-graded polynomial identities, and the
automorphisms group of P acts transitively on the maximal chains of P , we show
that A and B are graded isomorphic.
