The deformation bicomplex of a module algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module coalgebras, comodule (co)algebras, and (co)module bialgebras are also considered.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.97-128.