Abstract
Commutative clean rings and related rings have received much recent attention. A ring R is clean if each r ∈ R can be written r = u + e, where u is a unit and e an idempotent. This article deals mostly with the question: When is the classical ring of quotients of a commutative ring clean? After some general results, the article focuses on C(X) to characterize spaces X when Qcl(X) is clean. Such spaces include cozero complemented, strongly 0-dimensional and more spaces. Along the way, other extensions of rings are studied: directed limits and extensions by idempotents.
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