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Paper IPM / M / 537  


Abstract:  
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 zerodimensional, 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 zerodimensional.
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