关于余模范畴中的挠自由类与覆盖类  

On torsion free class and cover class in category of comodules

作　　者：李园 姚海楼[1] LI Yuan;YAO Hai-lou(College of Applied Sciences,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《山东大学学报（理学版）》2020年第8期1-5,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671126)。

摘　　要：对于一个余代数,首先引入了余模的(预)覆盖的概念并给出关于它的一些性质;然后,引入了极大倾斜余模和覆盖余模的概念,并证明倾斜挠自由类和极大倾斜余模之间存在一个双射;最后,得到了在余代数中当倾斜挠自由类是覆盖类时,它是由覆盖余模唯一表示的。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.

关 键 词：覆盖类 极大倾斜 挠自由类 覆盖余模 

分 类 号：O153.3[理学—数学]