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A Remark on Frobenius Extensions and Endomorphism Rings

Published online by Cambridge University Press:  22 January 2016

Tadasi Nakayama  and
Tosiro Tsuzuku
Tadasi Nakayama
Affiliation:
Mathematical Institute Nagoya University
Tosiro Tsuzuku
Affiliation:
Mathematical Institute Nagoya University
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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].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 15 , August 1959 , pp. 9 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[1] Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann. 127 (1954), 453–474.CrossRefGoogle Scholar
[2] Nakayama, T., On two topics in the struntural theory of rings (Galois theory of rings and Frobenius algebras), Proc. Intern. Cngrews of Math. (1950), II, 49.Google Scholar