  Given two algebras A and B, sometimes assumed to be C*-algebras, we consider
the question of putting algebra or C*-algebra structures on the tensor product
A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize
all possible such C*-algebra structures in terms of an action of the cyclic
group Z_2. An example related to commuting squares is also discussed.
