On the Set of Zero Divisors of a Topological
Ring
1967 ◽
Vol 10
(4)
◽
pp. 595-596
◽
Keyword(s):
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]).
1971 ◽
Vol 5
(2)
◽
pp. 271-274
◽
2016 ◽
Vol 16
(09)
◽
pp. 1750164
Keyword(s):
1969 ◽
Vol 6
(03)
◽
pp. 633-647
◽
1976 ◽
Vol 15
(3)
◽
pp. 453-454
◽
2012 ◽
Vol 05
(02)
◽
pp. 1250019
◽
Keyword(s):
2011 ◽
Vol 10
(04)
◽
pp. 741-753
◽
Keyword(s):
Keyword(s):