Open Access
SPRING 2014 Semiclean rings and rings of continuous functions
Nitin Arora, S. Kundu
J. Commut. Algebra 6(1): 1-16 (SPRING 2014). DOI: 10.1216/JCA-2014-6-1-1


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 $\c$.


Download Citation

Nitin Arora. S. Kundu. "Semiclean rings and rings of continuous functions." J. Commut. Algebra 6 (1) 1 - 16, SPRING 2014.


Published: SPRING 2014
First available in Project Euclid: 2 June 2014

zbMATH: 1294.16025
MathSciNet: MR3215558
Digital Object Identifier: 10.1216/JCA-2014-6-1-1

Primary: 13A99 , 13B30 , 16S60 , 54C40

Keywords: Clean rings , rings of continuous functions , Semiclean , Weakly clean

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.6 • No. 1 • SPRING 2014
Back to Top