Geodesic
On the Set of Zero Divisors of a TopologicalRing
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 595-596

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Let R be a topological (Hausdorff) ring such that for each a ∊ R, aR and Raare closed subsets of R. We will prove that if the set of non - trivialright (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 compactring. This theorem has an interesting corollary. Namely, if R is a discretering with a finite number of non - trivial left or right zero divisors thenR is a finite ring (Refer [1]). 
Koh, Kwangil. On the Set of Zero Divisors of a TopologicalRing. Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 595-596. doi: 10.4153/CMB-1967-058-5
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     author = {Koh, Kwangil},
     title = {On the {Set} of {Zero} {Divisors} of a {TopologicalRing}},
     journal = {Canadian mathematical bulletin},
     pages = {595--596},
     year = {1967},
     volume = {10},
     number = {4},
     doi = {10.4153/CMB-1967-058-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-058-5/}
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