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Modular Annihilator Algebras

Published online by Cambridge University Press:  20 November 2018

Bruce A. Barnes
Bruce A. Barnes*
Affiliation:
Cornell University and University of California, Berkeley
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In a recent paper (7) Yood developed the beginnings of a theory of modular annihilator algebras. In this paper we extend his work on these algebras.

The definition of modular annihilator algebra is algebraic in nature (see §4) ; in fact the algebra need not be assumed even topological. However, a significant number of important normed algebras are modular annihilator algebras. A list of examples is given in §8.

The theory of modular annihilator algebras is related to the theory of certain important topological algebras. In §5 we consider the relationships between dual and annihilator algebras and modular annihilator algebras, and in §7, the relationship between completely continuous normed algebras and modular annihilator algebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 566 - 578
Copyright
Copyright © Canadian Mathematical Society 1966

References

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7. Yood, B., Ideals in topological rings, Can. J. Math., 16 (1964), 28–45.Google Scholar