Let F = {Sr: r ∈ R} be a
disjoint family of semigroups. One says that F has a right zero union (RZU) if there
exists a semigroup S which is a disjoint union of the Sr where each Sr is a
left ideal of S. This paper gives some theorems on RZU of commutative
semigroups with special emphasis placed on commutative cancellative
semigroups.