关于拟Frobenius余环

On quasi-Frobenius corings

定义并研究了拟Frobenius余环,证明了下面几个等价条件:C是拟Frobenius余环;AC有限生成投射模,并且l:A→*C是Frobenius扩张;CA有限生成投射模,并且l:A→C*是Frobenius扩张;忘却函子Ur:Mc→MA是拟Frobenius函子;(Gl,Ul)与(Gr,Ur)都是拟左Frobenius函子偶;忘却函子U:cM→M是拟Frobenius函子.

In this paper, the notion of quasi - Frobenius corings is introduced. We prove that following conditions for a coring C are equivalent： C is a quasi - Frobenius coring; A C is finitely generated and projective, and the ring extension l：A→^＊C is a Frobenius; CA is finitely generated and projective, and the ring extension l：A →^＊ C is quasi - Frobenius ; the forgetful functor Ur ： M^c→ MA is quasi - Frobenius ; （ Gl, Ul ） and （ Gr,Ur） are left quasi - Frobenius functors pairs ;the forgetful functor Ul ：^cM →AM is quasi - Frobenius.