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Ideals in Topological Rings

Published online by Cambridge University Press:  20 November 2018

Bertram Yood
Bertram Yood*
Affiliation:
University of Oregon and Institute for Advanced Study
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We present here an investigation of the theory of one-sided ideals in a topological ring R. One of our aims is to discuss the question of "left" properties versus "right" properties. A problem of this sort is to decide if (a) all the modular maximal right ideals of R are closed if and only if all the modular maximal left ideals of R are closed. It is shown that this is the case if R is a quasi-Q-ring, that is, if R is bicontinuously isomorphic to a dense subring of a Q-ring (for the notion of a Q-ring see (6) or §2). All normed algebras are quasi-Q-rings. Also (a) holds if R is a semisimple ring with dense socle.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 28 - 45
Copyright
Copyright © Canadian Mathematical Society 1964

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