  In this paper, we study the connextion between lattice and Riesz
homomorphisms in Riesz spaces. We prove, under a certain condition, that any
lattice homomorphism on Riesz space is a Riesz homomorphism. This fits in the
type of results by Mena and Roth [7], thanh [9], Lochan and Strauss [5] and
Ercan and Wickstead [2].
