We prove, in this note, that a Zabavsky ring $R$ is an elementary divisor ring if and only if $R$ is a B'ezout ring. Many known results are thereby generalized to much wider class of rings, e.g. cite[Theorem 14]{4}, cite[Theorem 4]{6}, cite[Theorem 1.2.14]{9}, cite[Theorem 4]{11} and cite[Theorem 7]{12}.
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