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An element of a ring $R$ is called clean if it is the sum of a unit
and an idempotent and subset $A$ of $R$ is called clean if every
element of $A$ is clean. A topological characterization of clean elements
of $C(X)$ is given and it is shown that $C(X)$ is clean if and only
if $X$ is strongly zero-dimensional, if and only if there exists a
clean prime ideal in $C(X)$. We will also characterize topological
space $X$ for which the ideal $C_K(X)$ is clean.
Whenever $X$ is locally compact, it is shown that
$C_K(X)$ is clean if and only if $X$ is zero-dimensional.
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