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| 关于拟 Frobenius 余环 | |
| 引用本文： | 郭广泉. 关于拟 Frobenius 余环[J]. 安徽大学学报(自然科学版), 2007, 31(6): 10-12. DOI: 10.3969/j.issn.1000-2162.2007.06.003 |
| 作者姓名： | 郭广泉 |
| 作者单位： | 南京晓庄学院,数学系,江苏,南京,210017 |
| 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 Frobeniua 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:Mε→MA是拟 Frobenius 函子;(G1,U1)与(Gr,Ur) 都是拟左 Frobenius 函子偶;忘却函子Ul:εM→AM 是拟 Frobenius 函子. |
| 关 键 词： | 拟 Frobenius 余环 左拟 Frobenius 余环 左拟 Frobenius 函子偶 拟 Frobenius 函子 |
| 文章编号： | 1000-2162（2007）06-0010-03 |
| 收稿时间： | 2007-05-16 |
| 修稿时间： | 2007-05-16 |
On quasi-Frobenius corings |
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| GUO Guang-quan. On quasi-Frobenius corings[J]. Journal of Anhui University(Natural Sciences), 2007, 31(6): 10-12. DOI: 10.3969/j.issn.1000-2162.2007.06.003 | |
| Authors: | GUO Guang-quan |
| Abstract: | 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;AC 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:Mc→MA is quasi-Frobenius;(Gl,Ul) and(Gr,Ur) are left quasi-Frobenius functors pairs;the forgetful functor Ul:cM→AM is quasi-Frobenius. |
| Keywords: | quasi-Frobenius coring left quasi-Frobenius coring left quasi-Frobenius functor pairs quasi-Frobenius functor |
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