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We give a characterization of zero divisors of the ring Ca, b. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra Ca, b. We also characterize the zero divisors and topological divisors of zero in ^. Further, we show that zero is the only zero divisor in the disk algebra A (D) and that the class of singular elements in A (D) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of A (D) which are not zero divisors.
Chandra et al. (Thu,) studied this question.