关于拟Frobenius余环  

On quasi-Frobenius corings

作　　者：郭广泉[1] 

机构地区：[1]南京晓庄学院数学系,江苏南京210017

出　　处：《安徽大学学报（自然科学版）》2007年第6期10-12,共3页Journal of Anhui University(Natural Science Edition)

摘　　要：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.

关 键 词：拟Frobenius余环 左拟Frobenius余环 左拟Frobenius函子偶 拟Frobenius函子 

分 类 号：O153.3[理学—数学]