Radford Biproduct On (Bi)Hom-Hopf Algebras

In this thesis,we introduce and study Radford biproducts on(Bi)Hom-bialgebras.Specifically,we introduce the notion of the BiHom-smash coproduct and give the necessary and sufficient condition for the BiHom-smash product and BiHom-smash coproduct to form a BiHom-bialgebra,which further proves that BiHom-bialgebra is BiHom-Hopf algebra.Besides,we study the quasitriangular structure of Radford biproducts on Hombialgebras,and obtain the necessary and sufficient conditions for Radford biproducts Hom-bialgebras to form a quasitriangular Hom-bialgebra.