Access the full text.
Sign up today, get DeepDyve free for 14 days.
Jianlong Chen, Zhou Wang, Yiqiang Zhou (2009)
Rings in which elements are uniquely the sum of an idempotent and a unit that commuteJournal of Pure and Applied Algebra, 213
Lingling Fan, Xiande Yang (2006)
ON STRONGLY CLEAN MATRIX RINGSGlasgow Mathematical Journal, 48
Gautam Borooah, A. Diesl, T. Dorsey (2007)
Strongly clean triangular matrix rings over local ringsJournal of Algebra, 312
W. Burgess, P. Menal (1988)
On strongly πregular rings and homomorphisms into themCommunications in Algebra, 16
Xiande Yang, Yiqiang Zhou (2007)
Some families of strongly clean ringsLinear Algebra and its Applications, 425
Xiande Yang (2007)
Strongly clean rings and g(x)-clean rings
G. Ehrlich (1968)
Unit-regular ringsPortugaliae Mathematica, 27
Xiande Yang, Yiqiang Zhou (2008)
Strong cleanness of the $2\times 2$ matrix ring over a general local ringarXiv: Rings and Algebras
W. Nicholson (1977)
Lifting idempotents and exchange ringsTransactions of the American Mathematical Society, 229
G. Azumaya (1954)
Strongly π-regular ringsJ. Fac. Sci. Hokkaido Univ., 13
F. Cedó, L. Rowen (1998)
Addendum to “examples of semiperfect rings”Israel Journal of Mathematics, 107
I. Kaplansky (1950)
Topological representation of algebras. IITransactions of the American Mathematical Society, 68
S. Jain, S. Rizvi (1997)
Advances in Ring Theory
R. Arens, I. Kaplansky (1948)
Topological representation of algebrasTransactions of the American Mathematical Society, 63
Jianlong Chen, Xiande Yang, Yiqiang Zhou (2006)
When is the 2×2 matrix ring over a commutative local ring strongly clean?Journal of Algebra, 301
L. Gillman (1961)
Rings of continuous functions
F. Cedó, L.H. Rowen (1998)
Addendum to “Examples of semiperfect rings”, [Israel J. Math. 65 (1989), no. 3, 273–283]Isr. J. Math., 107
K. Brown, Hsiao-Lan Liu (1982)
Graduate Texts in Mathematics
V. Camillo, Dinesh Khurana (2001)
A CHARACTERIZATION OF UNIT REGULAR RINGSCommunications in Algebra, 29
W. Nicholson, Yiqiang Zhou (2005)
CLEAN RINGS: A SURVEY
F. Azarpanah (2002)
When is c(x) a Clean Ring?Acta Mathematica Hungarica, 94
P. Ara (1996)
Strongly -regular rings have stable range one, 124
Weixing Chen (2006)
A Question on Strongly Clean RingsCommunications in Algebra, 34
P. Cohn (1973)
Free rings and their relations
F. Couchot (2008)
Strong Cleanness of Matrix Rings Over Commutative RingsCommunications in Algebra, 36
W. McGovern (2003)
Clean Semiprime f-Rings with Bounded InversionCommunications in Algebra, 31
G. Azumaya (1951)
On Maximally Central AlgebrasNagoya Mathematical Journal, 2
Y. Hirano (1990)
Some Characterizations of π-Regular Rings of Bounded IndexMathematical journal of Okayama University, 32
J. Neumann (1936)
Regular ringsProc. Natl. Acad. Sci. U.S.A., 22
G. Azumaya (1954)
STRONGLY $\pi$-REGULAR RINGSHokkaido Mathematical Journal, 13
X. Yang, Y. Zhou (2008)
Strongly clean property of the 2×2 matrix ring over a general local ringJ. Algebra, 320
M. Nagata (1953)
On the Theory of Henselian RingsNagoya Mathematical Journal, 5
Jianlong Chen, Yiqiang Zhou (2007)
STRONGLY CLEAN POWER SERIES RINGSProceedings of the Edinburgh Mathematical Society, 50
Juncheol Han, W. Nicholson (2001)
EXTENSIONS OF CLEAN RINGSCommunications in Algebra, 29
Jianlong Chen, W. Nicholson, Yiqiang Zhou (2006)
Group rings in which every element is uniquely the sum of a unit and an idempotentJournal of Algebra, 306
P. Higgins, J. Mitchell, N. Ruškuc (2003)
GENERATING THE FULL TRANSFORMATION SEMIGROUP USING ORDER PRESERVING MAPPINGSGlasgow Mathematical Journal, 45
D. Eisenbud (1995)
Commutative Algebra: with a View Toward Algebraic Geometry
Y. Li (2007)
On strongly clean matrix ringsJ. Algebra, 312
F. Anderson, K. Fuller (1974)
Rings and Categories of Modules
Budh Nashier (1991)
Strongly regular ringsJournal of Algebra, 137
D. Anderson, V. Camillo (2002)
COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENTCommunications in Algebra, 30
A. Parshin (1999)
On a Ring of Formal Pseudo-differential OperatorsarXiv: Algebraic Geometry
F. Dischinger (1976)
Sur les anneaus fortement π-régliersC.R. Acad. Sci. Paris, 283
E. Armendariz, J. Fisher, R. Snider (1978)
On injective and surjective endomorphisms of finitely generated modulesCommunications in Algebra, 6
Jianlong Chen, Xiande Yang, Yiqiang Zhou (2006)
On Strongly Clean Matrix and Triangular Matrix RingsCommunications in Algebra, 34
N. McCoy (1939)
Generalized regular ringsBulletin of the American Mathematical Society, 45
J. Neumann (1936)
On Regular Rings.Proceedings of the National Academy of Sciences of the United States of America, 22
W. Nicholson (1999)
Strongly clean rings and fitting's lemmaCommunications in Algebra, 27
Yuanlin Li (2007)
Strongly clean matrix rings over local ringsJournal of Algebra, 312
Zhou Wang, Jianlong Chen (2004)
On two open problems about strongly clean ringsBulletin of the Australian Mathematical Society, 70
L. Rowen (1989)
Examples of semiperfect ringsIsrael Journal of Mathematics, 65
Gautam Borooah, A. Diesl, T. Dorsey (2008)
Strongly clean matrix rings over commutative local ringsJournal of Pure and Applied Algebra, 212
R. Engelking (1989)
General Topology
Let R be an associative ring with identity. An element a∈R is called clean if a=e+u with e an idempotent and u a unit of R and a is called strongly clean if, in addition, eu=ue. A ring R is called clean if every element of R is clean and R is strongly clean if every element of R is strongly clean. In the paper [Nicholson and Zhou, Clean rings: a survey, Advances in Ring Theory, 181–198, World Sci. Pub., Hackensack, NJ, 2005], the authors brought out an up to date account of the results in the study of clean rings. Here, we give an account of the results on strongly clean rings.
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 13, 2008
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.