# When is c(*x*) a Clean Ring?

Article

DOI: 10.1023/A:1015654520481

- Cite this article as:
- Azarpanah, F. Acta Mathematica Hungarica (2002) 94: 53. doi:10.1023/A:1015654520481

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## Abstract

An element of a ring *R* is called clean if it is the sum of a unit and an idempotent and a 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 spaces *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.

clean ringclean idealzero-dimensionalstrongly zero-dimensional

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© Kluwer Academic Publishers 2002