  We give an explicit description of the set of all factorization structures,
or twisting maps, existing between the algebras k^2 and k^2, and classify the
resulting algebras up to isomorphism. In the process we relate several
different approaches formerly taken to deal with this problem, filling a gap
that appeared in a recent paper by Cibils. We also provide a counterexample to
a result concerning the Hochschild (co)homology appeared in a paper by J.A.
Guccione and J.J. Guccione.
