群分次Frobenius余环

On group graded Frobenius corings

令G是一个群,A是一个环,C是群分次A-余环.定义了群分次Frobenius余环,这个概念是Frobenius余环概念的推广.给出群分次余环是群分次Frobenius余环的充分与必要条件,证明了群分次Frobenius余环是群分次环,并且A→Ce是Frobenius扩张.

Let G was a group, A a ring, Ca group graded A - coring. The notion of group graded Frobenius corings was defined, which generalised the notion of Frobenius coring. We found the necessary and sufficient conditions for a group graded coring was a group graded Frobenius coring. We proved that a group graded Frobenius corings was a ring, and A→Ce was Frobenius extension.