### On torsion free class and cover class in category of comodules

LI Yuan, YAO Hai-lou*

1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
• Published:2020-07-14

Abstract: For a coalgebra, the concept of(pre)covers for comodules is first introduced and some properties about them are given. Then, the concepts of maximal tilting comodules and cover comodules are given, and the existence of a bijection between the tilting torsion free classes and the maximal tilting comodules is proved. Finally, when the tilting torsion free class is a cover class, whose unique representation by cover comodules over a coalgebra is obtained.

CLC Number:

• O153.3
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