A Remark on Frobenius Extensions and Endomorphism Rings
A Remark on Frobenius Extensions and Endomorphism Rings
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DOI：
10.1017/s0027763000006644
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发表时间：
1959-08
影响因子：
0.8
通讯作者：
T. Nakayama;Tosiro Tsuzuku
中科院分区：
文献类型：
--
作者：
T. Nakayama;Tosiro Tsuzuku
在他的论文[1] F. Kasch发展了一个理论的Frobenius扩展作为推广的理论Frobenius代数。在其中，他建立了扩张的Frobenius性质与其自同态环的Frobenius性质之间的一个非常有趣的关系[1，Satz 5]，由此他进一步导出了单环的Galois扩张的Frobenius扩张性质[1，Satz 6];有了这些结果，他对那些被模糊地“警告”的东西作出了友好的回应。（如他所写）的一个作家之间的联系伽罗瓦理论和理论的弗罗贝纽斯代数[2]。
In his paper [1] F. Kasch developed a theory of Frobenius extensions as a generalization of the theory of Frobenius algebras. In it he established a very interesting relationship between the Frobenius property of an extension and that of its endomorphism ring [1, Satz 5], from which he further derived the Frobenius extension property of Galois extensions of simple rings [1, Satz 6]; with these results he kindly responded to what had been vaguely “conjectured” (as he wrote) by one of the writers on the connection between Galois theory and the theory of Frobenius algebras [2].