Characterization and multiplicative representation of homogeneous disjointness preserving polynomials

Let E and F be vector lattices and P:E → F an order bounded disjointness preserving s-homogeneous polynomial. P is said to be disjointness preserving if its corresponding symmetric S-linear operator from Es to F is disjointness preserving in each variable. In this article we give a caracterisation of disjointness preserving homogeneous orthogonally additive polynomials in vector lattices and prove multiplicative representation theorem for this class of polynomials.