Abstract
We give a construction of Rota–Baxter coalgebras from Hopf module coalgebras and also derive the structures of the pre-Lie coalgebras via Rota–Baxter coalgebras of different weight. Finally, the notion of Rota–Baxter bialgebra is introduced and some examples are provided.
Acknowledgements
The authors are deeply indebted to the referee for his/her very useful suggestions and some improvements to the original manuscript.
Notes
No potential conflict of interest was reported by the authors.