Advanced search
Publication Cover
Communications in Algebra Volume 27, 1999 - Issue 8
Submit an article Journal homepage
599
Views
130
CrossRef citations to date
0
Altmetric
Original Articles

Strongly clean rings and fitting's lemma

W. K. Nicholson Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada E-mail: [email protected]
Pages 3583-3592 | Received 01 Mar 1998, Published online: 27 Jun 2007

Citations (130)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (37)

R. Mohamadian. (2023) Almost clean elements in C(X). Quaestiones Mathematicae 46:9, pages 1937-1953.
Read now
Sharad Hegde. (2023) On uniquely clean elements. Communications in Algebra 51:5, pages 1835-1839.
Read now
T. Y. Lam. (2023) An introduction to q-central idempotents and q-abelian rings. Communications in Algebra 51:3, pages 1071-1088.
Read now
Ruhollah Barati, Ahmad Mousavi & Adel Abyzov. (2022) Rings whose elements are sums of m-potents and nilpotents. Communications in Algebra 50:10, pages 4437-4459.
Read now
Yasser Ibrahim & Mohamed Yousif. (2022) Perspectivity, exchange and summand-dual-square-free modules. Communications in Algebra 50:6, pages 2488-2506.
Read now
Liang Zhao, Cang Wu & Yao Wang. (2022) One-sided central Drazin inverses. Linear and Multilinear Algebra 70:7, pages 1193-1206.
Read now
Huihui Zhu, Liyun Wu & Qing-Wen Wang. (2022) Suitable elements, -clean elements and Sylvester equations in rings with involution. Communications in Algebra 50:4, pages 1535-1543.
Read now
Dinesh Khurana & Pace P. Nielsen. (2021) Perspectivity and von Neumann regularity. Communications in Algebra 49:12, pages 5483-5499.
Read now
S. Purkait. (2020) On strongly m-clean rings and m-semiperfect rings. Communications in Algebra 48:10, pages 4531-4541.
Read now
Jian Cui & Xiaobin Yin. (2020) Rings with 2-UJ property. Communications in Algebra 48:4, pages 1382-1391.
Read now
Sudipta Purkait, T. K. Dutta & Sukhendu Kar. (2020) On m-clean and strongly m-clean rings. Communications in Algebra 48:1, pages 218-227.
Read now
Janez Šter. (2019) Examples of strongly clean rings. Communications in Algebra 47:11, pages 4684-4696.
Read now
Alexander J. Diesl & Daniel R. Shifflet. (2018) Unifying strongly clean power series rings. Communications in Algebra 46:10, pages 4448-4462.
Read now
Yasser Ibrahim & Mohamed Yousif. (2018) Utumi modules. Communications in Algebra 46:2, pages 870-886.
Read now
Gaohua Tang & Yiqiang Zhou. (2017) An embedding theorem on triangular matrix rings. Linear and Multilinear Algebra 65:5, pages 882-890.
Read now
Ebrahim Ghashghaei & Warren Wm. McGovern. (2017) Fusible rings. Communications in Algebra 45:3, pages 1151-1165.
Read now
Dinesh Khurana, T.Y. Lam, PaceP. Nielsen & Yiqiang Zhou. (2015) Uniquely Clean Elements in Rings. Communications in Algebra 43:5, pages 1742-1751.
Read now
Qinghe Huang, Gaohua Tang & Yiqiang Zhou. (2014) Quasipolar Property of Generalized Matrix Rings. Communications in Algebra 42:9, pages 3883-3894.
Read now
Victor Camillo, ThomasJ. Dorsey & PaceP. Nielsen. (2014) Dedekind-Finite Strongly Clean Rings. Communications in Algebra 42:4, pages 1619-1629.
Read now
Jian Cui & Jianlong Chen. (2013) Characterizations of Quasipolar Rings. Communications in Algebra 41:9, pages 3207-3217.
Read now
Huanyin Chen. (2013) On Strongly Nil Clean Matrices. Communications in Algebra 41:3, pages 1074-1086.
Read now
Jian Cui & Jianlong Chen. (2012) A Class of Quasipolar Rings. Communications in Algebra 40:12, pages 4471-4482.
Read now
Huanyin Chen. (2012) Strongly J-Clean Matrices Over Local Rings. Communications in Algebra 40:4, pages 1352-1362.
Read now
Jian Cui & Jianlong Chen. (2012) Quasipolar Triangular Matrix Rings Over Local Rings. Communications in Algebra 40:2, pages 784-794.
Read now
Jian Cui & Jianlong Chen. (2011) When is a 2 × 2 Matrix Ring Over a Commutative Local Ring Quasipolar?. Communications in Algebra 39:9, pages 3212-3221.
Read now
Junchao Wei & Libin Li. (2010) Quasi-Normal Rings. Communications in Algebra 38:5, pages 1855-1868.
Read now
Lingling Fan & Xiande Yang. (2010) A Note on Strongly Clean Matrix Rings. Communications in Algebra 38:3, pages 799-806.
Read now
Lingling Fan & Xiande Yang. (2009) Strongly Clean Property and Stable Range One of Some Rings. Communications in Algebra 37:6, pages 2021-2029.
Read now
Hongbo Zhang. (2009) On Strongly Clean Modules. Communications in Algebra 37:4, pages 1420-1427.
Read now
Lingling Fan & Xiande Yang. (2008) On Rings Whose Elements are the Sum of a Unit and a Root of a Fixed Polynomial. Communications in Algebra 36:1, pages 269-278.
Read now
PaceP. Nielsen. (2006) Countable Exchange and Full Exchange Rings. Communications in Algebra 35:1, pages 3-23.
Read now
Jianlong Chen, Xiande Yang & Yiqiang Zhou. (2006) On Strongly Clean Matrix and Triangular Matrix Rings. Communications in Algebra 34:10, pages 3659-3674.
Read now
Weixing Chen. (2006) A Question on Strongly Clean Rings. Communications in Algebra 34:7, pages 2347-2350.
Read now
Guangshi Xiao & Wenting Tong. (2005) n-Clean Rings and Weakly Unit Stable Range Rings. Communications in Algebra 33:5, pages 1501-1517.
Read now
Huanyin Chen. (2004) Extensions of Unit-Regular Rings. Communications in Algebra 32:6, pages 2359-2364.
Read now
D. D. Anderson & V. P. Camillo. (2002) COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT. Communications in Algebra 30:7, pages 3327-3336.
Read now
Victor P. Camillo & Dinesh Khurana. (2001) A CHARACTERIZATION OF UNIT REGULAR RINGS. Communications in Algebra 29:5, pages 2293-2295.
Read now

Articles from other publishers (93)

Yanyuan Wang & Xinsong Yang. (2024) Rings in Which Every Element Is a Sum of a Nilpotent and Three 7-Potents. International Journal of Mathematics and Mathematical Sciences 2024, pages 1-14.
Crossref
Tufan Özdin. (2024) Characterization of $$*$$-(strongly) regular rings in terms of $${\mathcal {G}}$$-projections. Indian Journal of Pure and Applied Mathematics.
Crossref
Peter V. Danchev. (2021) A symmetric generalization of $$\pi $$-regular rings. Ricerche di Matematica 73:1, pages 179-190.
Crossref
Xavier Mary. (2023) On the structure of semigroups whose regular elements are completely regular. Semigroup Forum 107:3, pages 692-717.
Crossref
Gaohua Tang, Huadong Su & Pingzhi Yuan. (2021) Quasi-clean rings and strongly quasi-clean rings. Communications in Contemporary Mathematics 25:02.
Crossref
S. Kar & D. Das. (2022) Clean semiring. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 64:1, pages 197-207.
Crossref
Iulia-Elena Chiru, Septimiu Crivei & Gabriela Olteanu. (2023) Strongly regular matrices revisited. Linear Algebra and its Applications 658, pages 233-249.
Crossref
Huanyin Chen & Abdolyousefi SheibaniMarjanMarjan. (2023) New characterizations of g-Drazin inverse in a Banach algebra. Filomat 37:6, pages 1803-1813.
Crossref
A. N. Abyzov & D. T. Tapkin. (2021) On rings with xn − x nilpotent. Journal of Algebra and Its Applications 21:06.
Crossref
A. Mimouni. (2022) Note on clear rings. Afrika Matematika 33:2.
Crossref
Lu Cui, Linzhe Huang, Wenming Wu, Wei Yuan & Hanbin Zhang. (2022) On cleanness of von Neumann algebras. Journal of Mathematical Analysis and Applications 509:2, pages 125969.
Crossref
Dinesh Khurana. (2021) Lifting potent elements modulo nil ideals. Journal of Pure and Applied Algebra 225:11, pages 106762.
Crossref
Negin FARSHAD, Shaaban Ali SAFARİSABET & Ahmad MOUSSAVİ. (2021) Amalgamated rings with clean-type properties. Hacettepe Journal of Mathematics and Statistics 50:5, pages 1358-1370.
Crossref
P. A. Krylov, A. A. Tuganbaev & A. V. Tsarev. (2021) sp-Groups and Their Endomorphism Rings. Journal of Mathematical Sciences 256:3, pages 299-340.
Crossref
M. Tamer Koşan. (2020) Rings such that, for each unit u, u − u^n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics, pages 1-8.
Crossref
Jian Cui & Peter Danchev. (2019) Some new characterizations of periodic rings. Journal of Algebra and Its Applications 19:12, pages 2050235.
Crossref
Dinesh Khurana, T. Y. Lam, Pace P. Nielsen & Janez Šter. (2019) Special clean elements in rings. Journal of Algebra and Its Applications 19:11, pages 2050208.
Crossref
M. Tamer Koşan, Truong Cong Quynh & Jan Žemlička. (2019) UNJ-Rings. Journal of Algebra and Its Applications 19:09, pages 2050170.
Crossref
Xavier Mary. (2019) Characterizations of clean elements by means of outer inverses in rings and applications. Journal of Algebra and Its Applications 19:07, pages 2050134.
Crossref
I. Made Sulandra & Ichtiarida Mulyasari. Study on ring: g(x)-nil-clean and strongly g(x)-clean, but not strongly g(x)-nil-clean. Study on ring: g(x)-nil-clean and strongly g(x)-clean, but not strongly g(x)-nil-clean.
Marjan Sheibani Abdolyousefi, Nahid Ashrafi & Huanyin Chen. (2019) On Unit Nil-Clean Rings. Mediterranean Journal of Mathematics 16:4.
Crossref
Huihui Zhu, Honglin Zou & Pedro Patrício. (2019) Generalized inverses and their relations with clean decompositions. Journal of Algebra and Its Applications 18:07, pages 1950133.
Crossref
Cang Wu & Liang Zhao. (2019) Central Drazin inverses. Journal of Algebra and Its Applications 18:04, pages 1950065.
Crossref
Zhiling Ying & Mingming Fu. (2018) On Strongly $$J_n$$ J n -Clean Rings. Bulletin of the Iranian Mathematical Society 45:2, pages 627-639.
Crossref
A. N. Abyzov. (2019) Strongly q-Nil-Clean Rings. Siberian Mathematical Journal 60:2, pages 197-208.
Crossref
Jian Cui & Xiaobin Yin. (2018) A Generalization of Strongly Nil Clean Rings. Algebra Colloquium 25:04, pages 585-594.
Crossref
Jian Cui & Xiaobin Yin. (2018) On π-Regular Rings with Involution. Algebra Colloquium 25:03, pages 509-518.
Crossref
Janez Šter. (2018) On expressing matrices over as the sum of an idempotent and a nilpotent . Linear Algebra and its Applications 544, pages 339-349.
Crossref
Hani A. Khashan. (2018) On (weakly) precious rings associated to central polynomials. Boletim da Sociedade Paranaense de Matemática 36:2, pages 245.
Crossref
Tugce Pekacar Calci, Abdullah Harmanci & Burcu Ungor. (2016) An approach to quasipolarity for rings along nilpotent elements. Boletín de la Sociedad Matemática Mexicana 24:1, pages 95-106.
Crossref
Pace Nielsen & Janez Šter. (2017) Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings. Transactions of the American Mathematical Society 370:3, pages 1759-1782.
Crossref
Mete Burak Calci, Huanyin Chen, Sait Halicioglu & Abdullah Harmanci. (2017) Reversibility of Rings with Respect to the Jacobson Radical. Mediterranean Journal of Mathematics 14:3.
Crossref
Ali H. Handam & Hani A. Khashan. (2017) Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute. Open Mathematics 15:1, pages 420-426.
Crossref
Nahid Ashrafi & Ebrahim Nasibi. (2017) r-Clean Group Rings. Iranian Journal of Science and Technology, Transactions A: Science 41:1, pages 65-68.
Crossref
Long WANG & Junchao WEI. (2017) Some notes on $GQN$ rings. TURKISH JOURNAL OF MATHEMATICS 41, pages 1497-1509.
Crossref
G. Cǎlugǎreanu & T. Y. Lam. (2016) Fine rings: A new class of simple rings. Journal of Algebra and Its Applications 15:09, pages 1650173.
Crossref
Simion Breaz, Peter Danchev & Yiqiang Zhou. (2016) Rings in which every element is either a sum or a difference of a nilpotent and an idempotent. Journal of Algebra and Its Applications 15:08, pages 1650148.
Crossref
Dinesh Khurana, T. Y. Lam & Pace P. Nielsen. (2016) Exchange rings, exchange equations, and lifting properties. International Journal of Algebra and Computation 26:06, pages 1177-1198.
Crossref
Michael P. Drazin. (2016) On a result of J.J. Sylvester. Linear Algebra and its Applications 505, pages 361-366.
Crossref
Dinesh Khurana. (2016) Unit-Regularity of Regular Nilpotent Elements. Algebras and Representation Theory 19:3, pages 641-644.
Crossref
Simion Breaz & George Ciprian Modoi. (2016) Nil-clean companion matrices. Linear Algebra and its Applications 489, pages 50-60.
Crossref
Peter Danchev & Janez Šter. (2015) GENERALIZING $\pi$-REGULAR RINGS. Taiwanese Journal of Mathematics 19:6.
Crossref
Alexander J. Diesl, Thomas J. Dorsey, Wolf Iberkleid, Ramiro LaFuente-Rodriguez & Warren Wm. McGovern. (2015) Strongly clean triangular matrices over abelian rings. Journal of Pure and Applied Algebra 219:11, pages 4889-4906.
Crossref
Dinesh Khurana, T. Y. Lam & Pace P. Nielsen. (2015) Two-Sided Properties of Elements in Exchange Rings. Algebras and Representation Theory 18:4, pages 931-940.
Crossref
JIAN CUI & ZHOU WANG. (2015) A NOTE ON STRONGLY *-CLEAN RINGS. Journal of the Korean Mathematical Society 52:4, pages 839-851.
Crossref
M. Habibi, A. Moussavi & A. Alhevaz. (2015) On Skew Triangular Matrix Rings. Algebra Colloquium 22:02, pages 271-280.
Crossref
Yinchun Qu & Junchao Wei. (2014) Rings whose nilpotent elements form a Lie ideal. Studia Scientiarum Mathematicarum Hungarica 51:2, pages 271-284.
Crossref
Huanyin Chen. (2014) Strongly Clean Matrices over Commutative Domains. Algebra Colloquium 21:02, pages 257-266.
Crossref
Jian Cui & Xiaobin Yin. (2014) QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS. Bulletin of the Korean Mathematical Society 51:3, pages 813-822.
Crossref
JIAN CUI & JIANLONG CHEN. (2013) PSEUDOPOLAR MATRIX RINGS OVER LOCAL RINGS. Journal of Algebra and Its Applications 13:03, pages 1350109.
Crossref
Michael P. Drazin. (2014) Generalized inverses: Uniqueness proofs and three new classes. Linear Algebra and its Applications 449, pages 402-416.
Crossref
Alexander J. Diesl, Thomas J. Dorsey, Shelly Garg & Dinesh Khurana. (2014) A note on completeness and strongly clean rings. Journal of Pure and Applied Algebra 218:4, pages 661-665.
Crossref
Orhan Gurgun, Sait Halicioglu & Abdullah Harmanci. (2014) Nil-quasipolar rings. Boletín de la Sociedad Matemática Mexicana 20:1, pages 29-38.
Crossref
Nitin Arora & S. Kundu. (2014) Semiclean rings and rings of continuous functions. Journal of Commutative Algebra 6:1.
Crossref
Janez Šter. (2014) Weakly clean rings. Journal of Algebra 401, pages 1-12.
Crossref
HARPREET K. GROVER, ZHOU WANG, DINESH KHURANA, JIANLONG CHEN & T. Y. LAM. (2013) SUMS OF UNITS IN RINGS. Journal of Algebra and Its Applications 13:01, pages 1350072.
Crossref
Alexander J. Diesl & Thomas J. Dorsey. (2014) Strongly clean matrices over arbitrary rings. Journal of Algebra 399, pages 854-869.
Crossref
JIANLONG CHEN & JIAN CUI. (2013) TWO QUESTIONS OF L. VAŠ ON -CLEAN RINGS. Bulletin of the Australian Mathematical Society 88:3, pages 499-505.
Crossref
Gaohua Tang & Yiqiang Zhou. (2013) When is every linear transformation a sum of two commuting invertible ones?. Linear Algebra and its Applications 439:11, pages 3615-3619.
Crossref
Alexander J. Diesl. (2013) Nil clean rings. Journal of Algebra 383, pages 197-211.
Crossref
H. CHEN, O. GURGUN & H. KOSE. (2012) STRONGLY CLEAN MATRICES OVER COMMUTATIVE LOCAL RINGS. Journal of Algebra and Its Applications 12:01, pages 1250126.
Crossref
Huanyin Chen. (2013) ON 2 × 2 STRONGLY CLEAN MATRICES. Bulletin of the Korean Mathematical Society 50:1, pages 125-134.
Crossref
Gaohua Tang & Yiqiang Zhou. (2012) Strong cleanness of generalized matrix rings over a local ring. Linear Algebra and its Applications 437:10, pages 2546-2559.
Crossref
Zhou Wang & Jianlong Chen. (2012) Pseudo Drazin inverses in associative rings and Banach algebras. Linear Algebra and its Applications 437:6, pages 1332-1345.
Crossref
Huanyin Chen. (2012) STRONGLY NIL CLEAN MATRICES OVER R[x]/(x 2 -1) . Bulletin of the Korean Mathematical Society 49:3, pages 589-599.
Crossref
Pinar Aydogdu, Yang Lee & A. Cigdem Ozcan. (2012) RINGS CLOSE TO SEMIREGULAR. Journal of the Korean Mathematical Society 49:3, pages 605-622.
Crossref
Michael P. Drazin. (2012) A class of outer generalized inverses. Linear Algebra and its Applications 436:7, pages 1909-1923.
Crossref
CHUNNA LI & YIQIANG ZHOU. (2012) ON STRONGLY *-CLEAN RINGS. Journal of Algebra and Its Applications 10:06, pages 1363-1370.
Crossref
Dinesh Khurana, T.Y. Lam & Zhou Wang. (2011) Rings of square stable range one. Journal of Algebra 338:1, pages 122-143.
Crossref
Lia Vaš. (2010) ⁎-Clean rings; some clean and almost clean Baer ⁎-rings and von Neumann algebras. Journal of Algebra 324:12, pages 3388-3400.
Crossref
Bingjun Li & Lianggui Feng. (2010) f-CLEAN RINGS AND RINGS HAVING MANY FULL ELEMENTS. Journal of the Korean Mathematical Society 47:2, pages 247-261.
Crossref
Xiande Yang. (2008) A Survey of Strongly Clean Rings. Acta Applicandae Mathematicae 108:1, pages 157-173.
Crossref
Jianlong Chen, Zhou Wang & Yiqiang Zhou. (2009) Rings in which elements are uniquely the sum of an idempotent and a unit that commute. Journal of Pure and Applied Algebra 213:2, pages 215-223.
Crossref
TSIU-KWEN LEE & YIQIANG ZHOU. (2008) A CLASS OF EXCHANGE RINGS. Glasgow Mathematical Journal 50:3, pages 509-522.
Crossref
Xiande Yang & Yiqiang Zhou. (2008) Strong cleanness of the matrix ring over a general local ring . Journal of Algebra 320:6, pages 2280-2290.
Crossref
Gautam Borooah, Alexander J. Diesl & Thomas J. Dorsey. (2008) Strongly clean matrix rings over commutative local rings. Journal of Pure and Applied Algebra 212:1, pages 281-296.
Crossref
Xiande Yang & Yiqiang Zhou. (2007) Some families of strongly clean rings. Linear Algebra and its Applications 425:1, pages 119-129.
Crossref
Yuanlin Li. (2007) Strongly clean matrix rings over local rings. Journal of Algebra 312:1, pages 397-404.
Crossref
Gautam Borooah, Alexander J. Diesl & Thomas J. Dorsey. (2007) Strongly clean triangular matrix rings over local rings. Journal of Algebra 312:2, pages 773-797.
Crossref
Huan Yin Chen. (2006) Exchange Rings Generated by Their Units. Acta Mathematica Sinica, English Series 23:2, pages 357-364.
Crossref
Weixing Chen. (2007) On Semiabelian π-Regular Rings. International Journal of Mathematics and Mathematical Sciences 2007, pages 1-10.
Crossref
B. Goldsmith, C. Meehan & S.L. Wallutis. (2007) Torsion-free groups and modules with the involution property. Journal of Pure and Applied Algebra 208:1, pages 127-134.
Crossref
Guangshi Xiao & Wenting Tong. (2012) n-Clean Rings. Algebra Colloquium 13:04, pages 599-606.
Crossref
V.P. Camillo, D. Khurana, T.Y. Lam, W.K. Nicholson & Y. Zhou. (2006) Continuous modules are clean. Journal of Algebra 304:1, pages 94-111.
Crossref
Jianlong Chen, Xiande Yang & Yiqiang Zhou. (2006) When is the matrix ring over a commutative local ring strongly clean? . Journal of Algebra 301:1, pages 280-293.
Crossref
Myung-Sook Ahn & D.D. Anderson. (2006) Weakly Clean Rings and Almost Clean Rings. Rocky Mountain Journal of Mathematics 36:3.
Crossref
Huanyin Chen & Miaosen Chen. (2006) REGULAR ELEMENTS WHICH IS A SUM OF AN IDEMPOTENT AND A LEFT CANCELLABLE ELEMENT. Taiwanese Journal of Mathematics 10:4.
Crossref
Shuqin Wang & Huanyin Chen. (2006) BOUNDED MATRICES OVER REGULAR RINGS. Bulletin of the Korean Mathematical Society 43:1, pages 1-7.
Crossref
Weixing Chen. (2006) -clean rings . International Journal of Mathematics and Mathematical Sciences 2006, pages 1-7.
Crossref
Huanyin Chen & Miaosen Chen. (2005) Extensions of GM-rings. Czechoslovak Mathematical Journal 55:2, pages 273-281.
Crossref
Huanyin Chen & Miaosen Chen. (2005) On strongly Π-regular ideals. Journal of Pure and Applied Algebra 195:1, pages 21-32.
Crossref
Zhou Wang & Jianlong Chen. (2009) On two open problems about strongly clean rings. Bulletin of the Australian Mathematical Society 70:2, pages 279-282.
Crossref
Dinesh Khurana & T.Y. Lam. (2004) Clean matrices and unit-regular matrices. Journal of Algebra 280:2, pages 683-698.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.