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Advances in Mathematical Physics
Volume 2017, Article ID 4653172, 14 pages
https://doi.org/10.1155/2017/4653172
Research Article

The Factorization for a Class of Hom-Coalgebras

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Correspondence should be addressed to Lihong Dong; moc.liamg@0102gnodgnohil

Received 15 May 2017; Revised 10 August 2017; Accepted 7 September 2017; Published 29 October 2017

Academic Editor: Yao-Zhong Zhang

Copyright © 2017 Lihong Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a Hom-Hopf algebra and a Hom-coalgebra. In this paper, we first introduce the notions of Hom-crossed coproduct and cleft coextension and then discuss the equivalence between them. Furthermore, we discuss the relation between cleft coextension and Hom-module coalgebra with the Hom-Hopf module structure and obtain a Hom-coalgebra factorization for Hom-module coalgebra with the Hom-Hopf module structure.