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Communications in Algebra Volume 34, 2006 - Issue 10
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Original Articles

On Strongly Clean Matrix and Triangular Matrix Rings

Jianlong Chen Department of Mathematics, Southeast University, Nanjing, China
,
Xiande Yang Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Canada
&
Yiqiang Zhou Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, CanadaCorrespondence[email protected]
Pages 3659-3674 | Received 01 Mar 2005, Published online: 16 Jan 2007

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M. Ahmadi & A. Moussavi. (2020) Rings whose singular ideals are nil. Communications in Algebra 48:11, pages 4796-4808.
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Sudipta Purkait, T. K. Dutta & Sukhendu Kar. (2020) On m-clean and strongly m-clean rings. Communications in Algebra 48:1, pages 218-227.
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Alexander J. Diesl & Daniel R. Shifflet. (2018) Unifying strongly clean power series rings. Communications in Algebra 46:10, pages 4448-4462.
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Sushma Singh & Om Prakash. (2018) A note on lower nil M-Armendariz rings. Cogent Mathematics & Statistics 5:1.
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K. Paykan & M. Habibi. (2018) Further results on skew monoid rings of a certain free monoid (I). Cogent Mathematics & Statistics 5:1.
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Tamer Koşan, Serap Sahinkaya & Yiqiang Zhou. (2017) On weakly clean rings. Communications in Algebra 45:8, pages 3494-3502.
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Gaohua Tang & Yiqiang Zhou. (2017) An embedding theorem on triangular matrix rings. Linear and Multilinear Algebra 65:5, pages 882-890.
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Abdollah Alhevaz & Dariush Kiani. (2016) Annihilator Ideals of Noncommutative Ring Constructions. Communications in Algebra 44:1, pages 63-86.
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Qinghe Huang, Gaohua Tang & Yiqiang Zhou. (2014) Quasipolar Property of Generalized Matrix Rings. Communications in Algebra 42:9, pages 3883-3894.
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M. Habibi & A. Moussavi. (2014) Annihilator Properties of Skew Monoid Rings. Communications in Algebra 42:2, pages 842-852.
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A. Alhevaz & D. Kiani. (2014) On Zero-Divisors in Skew Inverse Laurent Series Over NonCommutative Rings. Communications in Algebra 42:2, pages 469-487.
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A. Alhevaz & A. Moussavi. (2014) On Monoid Rings Over Nil Armendariz Ring. Communications in Algebra 42:1, pages 1-21.
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Jian Cui & Jianlong Chen. (2013) Characterizations of Quasipolar Rings. Communications in Algebra 41:9, pages 3207-3217.
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A. Alhevaz & D. Kiani. (2013) Radicals of Skew Inverse Laurent Series Rings. Communications in Algebra 41:8, pages 2884-2902.
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M. Habibi, A. Moussavi & A. Alhevaz. (2013) The McCoy Condition on Ore Extensions. Communications in Algebra 41:1, pages 124-141.
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M. Habibi, A. Moussavi & S. Mokhtari. (2012) On Skew Armendariz of Laurent Series Type Rings. Communications in Algebra 40:11, pages 3999-4018.
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Jian Cui & Jianlong Chen. (2012) Quasipolar Triangular Matrix Rings Over Local Rings. Communications in Algebra 40:2, pages 784-794.
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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.
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Huanyin Chen. (2010) On Strongly J-Clean Rings. Communications in Algebra 38:10, pages 3790-3804.
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Mohammad Habibi, Kamal Paykan & Hassan Arianpoor. (2023) On generalized quasi Baer skew monoid rings. Journal of Algebra and Its Applications 23:06.
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Gaohua Tang, Huadong Su & Pingzhi Yuan. (2021) Quasi-clean rings and strongly quasi-clean rings. Communications in Contemporary Mathematics 25:02.
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Yiqiang Zhou. (2021) A multiplicative dual of nil-clean rings. Canadian Mathematical Bulletin 65:1, pages 39-43.
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Érica Z. Fornaroli. (2021) Jordan isomorphisms of skew incidence rings. Journal of Algebra and Its Applications 20:03, pages 2150034.
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Kamal Paykan. (2016) Some New Results on Skew Triangular Matrix Rings with Constant Diagonal. Vietnam Journal of Mathematics 45:4, pages 575-584.
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Kamal Paykan & Ahmad Moussavi. (2017) McCoy property and nilpotent elements of skew generalized power series rings. Journal of Algebra and Its Applications 16:10, pages 1750183.
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Kamal Paykan & Ahmad Moussavi. (2017) The McCoy condition on skew monoid rings. Asian-European Journal of Mathematics 10:03, pages 1750050.
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Kamal Paykan & Ahmad Moussavi. (2016) Nilpotent elements and nil-Armendariz property of skew generalized power series rings. Asian-European Journal of Mathematics 10:02, pages 1750034.
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A. Moussavi. (2016) On Radicals of Skew Inverse Laurent Series Rings. Algebra Colloquium 23:02, pages 335-346.
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K. Paykan & A. Moussavi. (2016) Quasi-Armendariz generalized power series rings. Journal of Algebra and Its Applications 15:05, pages 1650086.
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Mohammad Habibi. (2015) On Armendariz Rings of Inverse Skew Laurent Series Type. Algebra Colloquium 22:spec01, pages 799-816.
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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.
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Mohammad Habibi & Ahmad Moussavi. (2015) Special properties of a skew triangular matrix ring with constant diagonal. Asian-European Journal of Mathematics 08:03, pages 1550021.
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M. Habibi, A. Moussavi & A. Alhevaz. (2015) On Skew Triangular Matrix Rings. Algebra Colloquium 22:02, pages 271-280.
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Huanyin Chen. (2014) Strongly Clean Matrices over Commutative Domains. Algebra Colloquium 21:02, pages 257-266.
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Jian Cui & Xiaobin Yin. (2014) QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS. Bulletin of the Korean Mathematical Society 51:3, pages 813-822.
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JIAN CUI & JIANLONG CHEN. (2013) PSEUDOPOLAR MATRIX RINGS OVER LOCAL RINGS. Journal of Algebra and Its Applications 13:03, pages 1350109.
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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.
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A. ALHEVAZ & D. KIANI. (2013) McCOY PROPERTY OF SKEW LAURENT POLYNOMIALS AND POWER SERIES RINGS. Journal of Algebra and Its Applications 13:02, pages 1350083.
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Alexander J. Diesl & Thomas J. Dorsey. (2014) Strongly clean matrices over arbitrary rings. Journal of Algebra 399, pages 854-869.
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MOHAMMAD HABIBI & RAOUFEH MANAVIYAT. (2013) A GENERALIZATION OF NIL-ARMENDARIZ RINGS. Journal of Algebra and Its Applications 12:06, pages 1350001.
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Alexander J. Diesl. (2013) Nil clean rings. Journal of Algebra 383, pages 197-211.
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Huanyin Chen. (2013) ON 2 × 2 STRONGLY CLEAN MATRICES. Bulletin of the Korean Mathematical Society 50:1, pages 125-134.
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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.
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M. HABIBI & A. MOUSSAVI. (2012) NILPOTENT ELEMENTS AND NIL-ARMENDARIZ PROPERTY OF MONOID RINGS. Journal of Algebra and Its Applications 11:04, pages 1250080.
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M. Habibi & A. Moussavi. (2012) ON NIL SKEW ARMENDARIZ RINGS. Asian-European Journal of Mathematics 05:02, pages 1250017.
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Xiande Yang. (2008) A Survey of Strongly Clean Rings. Acta Applicandae Mathematicae 108:1, pages 157-173.
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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.
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Xiande Yang & Yiqiang Zhou. (2008) Strong cleanness of the matrix ring over a general local ring . Journal of Algebra 320:6, pages 2280-2290.
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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.
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Xiande Yang & Yiqiang Zhou. (2007) Some families of strongly clean rings. Linear Algebra and its Applications 425:1, pages 119-129.
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Yuanlin Li. (2007) Strongly clean matrix rings over local rings. Journal of Algebra 312:1, pages 397-404.
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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.
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