中文摘要：

设H为双代数，并且对余代数C有弱余作用ρ．设α：C→H⊙H是一个线性映射，D是一个右H-余模余代数．给出一种交叉双积双代数结构C口^αH口D，著名的Radford双积和Majiddouble双积是其特例．另外还得到了Brzezindki交叉余积和smash积构成Hopf代数的充分必要条件．

英文摘要：

Let H be a bialgebra, with a weak coaction ρ on the coalgebra C. Let α：C→H⊙H be a linear map, and D a right H-comodule coalgebra, we obtain a construction of crossed hiproduct bialgebra, and the celebrated Radford＇s biproduct and Majid＇s double hiproduct are both derived as special cases. Furthermore, necessary and sufficient conditions for Brzezinki＇s crossed coproduct equipped with smash product to be a Hopf algebra are given.