Let
E
E
and
F
F
be Riesz spaces and
T
1
,
T
2
,
…
,
T
n
{T_1},{T_2}, \ldots ,{T_n}
be linear lattice homomorphisms (henceforth called lattice homomorphisms) from
E
E
to
F
F
. If
T
=
∑
i
=
1
n
T
i
T = \sum \nolimits _{i = 1}^n {{T_i}}
, then it is easy to check that
T
T
is positive and that if
x
0
,
x
1
,
…
x
n
∈
E
{x_0},{x_1}, \ldots {x_n} \in E
and
x
i
∧
x
j
=
0
{x_i} \wedge {x_j} = 0
for all
i
≠
j
i \ne j
, then
∧
i
=
0
n
T
x
i
=
0
\wedge _{i = 0}^nT{x_i} = 0
. The purpose of this note is to show that if
F
F
is Dedekind complete, the above necessary condition for
T
T
to be be the sum of
n
n
lattice homomorphisms is also sufficient. The result extends to sums of disjointness preserving operators, thereby leading to a characterization of the ideal of order bounded operators generated by the lattice homomorphisms.