Some Remarks on Symmetric and Frobenius Algebras
- 1 February 1960
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 16, 65-71
- https://doi.org/10.1017/s0027763000007558
Abstract
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.Keywords
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