关键词: smash积, 对极, 基本结构定理, ×_R-Hopf代数

Abstract: It is proved that the category of the left comodules over the ×_R-bialgebra L is equivalent to the category of the left L^*-modules, and the monoidal functor from ^L_AM to A#L^*-module is equivalent.For the ×_R-Hopf algebras the generalization of the fundamental structure theorem of Hopf modules is given by introducing the definition of antipode.

Key words: ×_R-Hopf algebra, smash product, antipode, fundamental structure theorem