Abstract
As defined by Ye [{\bf12}], a ring is semiclean if every element is the sum of a unit and a periodic element. Ahn and Anderson [{\bf1}] called a ring {weakly clean} if every element can be written as $u+e$ or $u-e$, where $u$ is a unit and $e$ an idempotent. A weakly clean ring is {semiclean}. We show the existence of semiclean rings that are not weakly clean. Every semiclean ring is $2$-clean. New classes of semiclean subrings of $\r$ and $\c$ are introduced and conditions are given when these rings are clean. Cleanliness and related properties of $C(X,A)$ are studied when $A$ is a dense semiclean subring of $\r$ or $\c$.
Citation
Nitin Arora. S. Kundu. "Semiclean rings and rings of continuous functions." J. Commut. Algebra 6 (1) 1 - 16, SPRING 2014. https://doi.org/10.1216/JCA-2014-6-1-1
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