中文摘要：

在Brzezinski T（2002）A-上环的基础上介绍了C-环的基本概念，C是一个余代数．分析了C-环及其模范畴的结构，并构造了C-环的例子．研究了C-环中的两个主要函子：忘却函子F：MA→M^C肼和导出函子-□cA：M^C→MA．并且讨论了两个函子可分的条件以及这两个函子的伴随情况．其次结合伽罗华理论将上环的一些主要性质推广到C-环，进而得到了C-环中的一些有意义的结论．

英文摘要：

Base on the paper[1], the notion of a coring-C-ring is introduced, which is a coalgebra, An examples of C-ring is given. The forgetful functor from the category of right modules of an C-ring A to the category of right C-comodules and the introduction functor -□cA of C-ring are studied. The conditions of when these functors are separable and the properties of adjoint of these functors are studied also. Finally, the Galois theory is applied to matrix C-ring to obtain some useful results.