We study the Morita equivalence classes of crossed products of rotation algebras A_, where is a rational number, by finite and infinite cyclic subgroups of SL (2, Z). We show that for any such subgroup F, the crossed products A_ F and A' F are strongly Morita equivalent, where both and ' are rational. Combined with previous results for irrational values of, our result provides a complete classification of the crossed products A_ F up to Morita equivalence.
Chakraborty et al. (Mon,) studied this question.