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On the Set of Zero Divisors of a Topological Ring
Published online by Cambridge University Press: 20 November 2018
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Let R be a topological (Hausdorff) ring such that for each a ∊ R, aR and Ra are closed subsets of R. We will prove that if the set of non - trivial right (left) zero divisors of R is a non-empty set and the set of all right (left) zero divisors of R is a compact subset of R, then R is a compact ring. This theorem has an interesting corollary. Namely, if R is a discrete ring with a finite number of non - trivial left or right zero divisors then R is a finite ring (Refer [1]).
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- Research Article
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- Copyright © Canadian Mathematical Society 1967
References
1.
Ganesan, N., “Properties of Rings with a finite Number of Zero
Divisors II”, Math Annalen
161, 241-246
(1966).Google Scholar
2.
Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis. Vol.
I, Springer-Verlag,
Berlin
1963.Google Scholar
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