Acta Mathematica Hungarica

, Volume 94, Issue 1, pp 53–58

When is c(x) a Clean Ring?

Authors

  • F. Azarpanah
    • DEPARTMENT OF MATHEMATICSCHAMRAN UNIVERSITY AHVAZ
Article

DOI: 10.1023/A:1015654520481

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

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 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.

clean ringclean idealzero-dimensionalstrongly zero-dimensional

Copyright information

© Kluwer Academic Publishers 2002