关于Frobenius函子的一个注记（英文）  

A note on Frobenius functors

作　　者：赵志兵[1] ZHAO Zhibing(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《中国科学技术大学学报》2018年第8期618-621,共4页JUSTC

基　　金：Supported by Natural Science Foundation of China(11571329);the Natural Science Foundation of Anhui Province(1708085MA01);Project of University Natural Science Research of Anhui Province(KJ2015A101)

摘　　要：利用Frobenius函子来刻画Frobenius双模.证明了一个双模是Frobenius的当且仅当它作为左模和右模均是有限生成投射的,并且所对应的函子限制到有限生成投射模类上是一个Frobenius函子.利用这种刻画,得到了关于经典的自同态环定理的一种新的利用函子方法的证明.Some new characterizations of Frobenius bimodules in terms of Frobenius functors were given.It was proved that a bimodule is Frobenius if and only if it is finitely generated projective on both sides,and that the restriction of the corresponding tensor functor to the categories of finitely generated projective modules is a Frobenius functor.The characterizations allow us to give a new proof of the endomorphism ring theorem by a functorial method.

关 键 词：Frobenius函子 Frobenius扩张 自同态环定理 

分 类 号：O153.3[理学—数学]