Generalized Hopf Ore Expansion Of Hopf Group Co-algebras

In this paper, we study the generalized Hopf Ore extensions of Hopf group coalgebras.Firstly, the concepts of Ore extensions, Hopf Ore extensions and Hopf group coalgebras are introduced. Secondly, the definition of generalized Hopf Ore extensions over Hopf group coalgebras is given, and the necessary and sufficient conditions for the generalized Hopf Ore extensions of Hopf group coalgebras to become Hopf group coalgebras are giv-en. Finally, we discuss and study the isomorphism between two generalized Hopf Ore extensions of Hopf group coalgebras.