The concepts of the generalization cleft comodule algebra and thegeneralization H?Galois extension with a nouial basis were due to Masuokaand Doi [MD], they studied the equivalence of them and the dual case. Butthey didn?

• Masuoka和Doi[MD]给出了广义cleft余模代数和具有一个正规基的广义H-Galois扩张的概念，他们研究了二者的等价及对偶情形，但没有涉及到Hopfcrossed积或余积。