For commutative Banach algebrasBandIand a continuous representation π:B→ M(I), where M(I) are those bounded linear operatorsT: I → Ithat satisfyT(ij) =iT(j) for alli,jεI, the direct sumBIcan be made into a commutative Banach algebra which containsBandIas respectively a closed subalgebra and a closed ideal. This algebra is called the semidirect product ofBandI. Some topological aspects of the character space of a semidirect product are described. Furthermore, decompositions of commutative Banach algebras into the direct sum of a subalgebra and a principal ideal are investigated.