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Some Remarks on Symmetric and Frobenius Algebras

Published online by Cambridge University Press:  22 January 2016

J. P. Jans
J. P. Jans*
Affiliation:
University of Washington
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In [5] we defined the concepts of Frobenius and symmetric algebra for algebras of infinite vector space dimension over a field. It was shown there that with the introduction of a topology and the judicious use of the terms continuous and closed, many of the classical theorems of Nakayama [7, 8] on Frobenius and symmetric algebras could be generalized to the infinite dimensional case. In this paper we shall be concerned with showing certain algebras are (or are not) Frobenius or symmetric. In Section 3, we shall see that an algebra can be symmetric or Frobenius in “many ways”. This is a problem which did not arise in the finite dimensional case.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 65 - 71
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Cohn, P. M., On a Class of Simple Rings, Mathematika, vol. 5 (1958), pp. 103–117.CrossRefGoogle Scholar
[2] Jacobson, N., Structure of Rings, Am. Math. Soc. Coll. Pub. XXXVII (1956).Google Scholar
[3] Jans, J. P., On Segregated Rings and Algebras, Nagoya Math. Jour., vol. 11 (1957), pp. 1–7.CrossRefGoogle Scholar
[4] Jans, J. P., Compact Rings with Open Radical, Duke Math. Jour. vol. 24 (1957), pp. 573–578.CrossRefGoogle Scholar
[5] Jans, J. P., On Frobenius Algebras, Annals of Math. vol. 69 (1959), pp. 392–407.CrossRefGoogle Scholar
[6] Jans, J. P. and Nakayama, T., On the Dimensional of Modules and Algebras, VII, Nagoya Math. Jour. Vol. 11 (1957), pp. 67–76.CrossRefGoogle Scholar
[7] Nakayama, T., On Frobenius Algebras I, Annals of Math. vol. 40 (1939), pp. 611–633.CrossRefGoogle Scholar
[8] Nakayama, T., On Frobenius Algebras II, Annals of Math. vol. 42 (1941), pp. 1–21.CrossRefGoogle Scholar