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Paper   IPM / M / 537
School of Mathematics
  Title:   When is C(X) a clean ring?
  Author(s):  F. Azarpanah
  Status:   Published
  Journal: Acta Math. Hungar.
  No.:  1-2
  Vol.:  94
  Year:  2002
  Pages:   53-58
  Supported by:  IPM
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 CK(X) is clean. Whenever X is locally compact, it is shown that CK(X) is clean if and only if X is zero-dimensional.

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