When is c(x) a Clean Ring?
- F. Azarpanah
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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 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 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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- When is c(x) a Clean Ring?
Acta Mathematica Hungarica
Volume 94, Issue 1-2 , pp 53-58
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- clean ring
- clean ideal
- strongly zero-dimensional
- F. Azarpanah (1)
- Author Affiliations
- 1. DEPARTMENT OF MATHEMATICS, CHAMRAN UNIVERSITY AHVAZ, IRAN