Abstract
In this paper we unify the structures of various clean rings by introducing the notion of
Open Access
P
Received20 Mar 2006
Accepted21 Mar 2006
Published13 Jun 2006
References
D. D. Anderson and V. P. Camillo, “Commutative rings whose elements are a sum of a unit and idempotent,” Communications in Algebra, vol. 30, no. 7, pp. 3327–3336, 2002.
View at: Publisher Site | Google Scholar | MathSciNetV. P. Camillo and H.-P. Yu, “Exchange rings, units and idempotents,” Communications in Algebra, vol. 22, no. 12, pp. 4737–4749, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Chen, “A note on polynomial rings,” submitted for publication.
View at: Google ScholarJ. Han and W. K. Nicholson, “Extensions of clean rings,” Communications in Algebra, vol. 29, no. 6, pp. 2589–2595, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetW. K. Nicholson, “Lifting idempotents and exchange rings,” Transactions of the American Mathematical Society, vol. 229, pp. 269–278, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. K. Nicholson, “Strongly clean rings and Fitting's lemma,” Communications in Algebra, vol. 27, no. 8, pp. 3583–3592, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Samei, “Clean elements in commutative reduced rings,” Communications in Algebra, vol. 32, no. 9, pp. 3479–3486, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG. Xiao and W. Tong, “-clean rings and weakly unit stable range rings,” Communications in Algebra, vol. 33, no. 5, pp. 1501–1517, 2005.
View at: Google Scholar | MathSciNetY. Ye, “Semiclean rings,” Communications in Algebra, vol. 31, no. 11, pp. 5609–5625, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. B. Zhang and W. Tong, “Generalized clean rings,” submitted for publication.
View at: Google Scholar
Copyright
Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.