In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is called the Hom-dimodule is introduced and its properties are discussed Moreover the category of Hom-dimodules in connection with the Hom D-equation R12 R23 =R23 R12 for R∈Endk M⊙M and a Hom-module M is investigated.Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.
