In this paper the structure
theory of convolution measure algebras due to J. L. Taylor is used in studying the
multiplier algebra M(A) of a commutative semi-simple convolution measure algebra
A. A criterion is given for the embeddability of M(A) in the measure algebra M(S)
on the structure semigroup S of A, and the relationship between the structure
semigroups of A and M(A) is investigated in case M(A) is also a convolution
measure algebra and S has an identity.