JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (12): 16-24.doi: 10.6040/j.issn.1671-9352.0.2017.153

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Nil *-clean rings

WANG Hui-xing, CUI Jian*, CHEN Yi-ning   

  1. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2017-04-12 Online:2017-12-20 Published:2017-12-22

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Abstract: The concepts of nil *-clean rings and uniquely nil *-clean rings are introduced. Basic properties and extension properties of such rings are investigated. Moreover, the relations of several classes of *-rings are discussed.

Key words: *-clean ring, nil *-clean ring, uniquely nil *-clean ring, nil clean ring

CLC Number: 

  • O153.3
[1] NICHOLSON W K. Lifting idempotents and exchange rings[J]. Transactions of the American Mathematical Society, 1977, 229:269-278.
[2] NICHOLSON W K, ZHOU Y Q. Clean rings: a survey[M] // Advances in Ring Theory. 2005:181-198.
[3] CAMILLO V P, YU H P. Exchange rings, units and idempotents[J]. Communications in Algebra, 1994, 22(12):4737-4749.
[4] DIESL A J. Nil clean rings[J]. Journal of Algebra, 2013, 383:197-211.
[5] KOSAN T, WANG Z, ZHOU Y. Nil-clean and strongly nil-clean rings[J]. Journal of Pure and Applied Algebra, 2016, 220(2):633-646.
[6] BREAZ S, GALUGAREANU G, DANCHEV P, et al. Nil-clean matrix rings[J]. Linear Algebra and Its Applications, 2013, 439(10):3115-3119.
[7] CHEN H, SHEIBANI M. On strongly nil clean rings[J]. Communications in Algebra, 2017, 45(4):1719-1726.
[8] VAS L. *-clean rings; some clean and almost clean Baer *-rings and von Neumann algebras[J]. Journal of Algebra, 2010, 324(12):3388-3400.
[9] HARMANCI A, CHEN H, OZCAN A C. Strongly nil-*-clean rings[J]. Journal of Algebra Combinatorics Discrete Structures and Applications, 2017, 2:155-164.
[10] UNGOR B, GURGUN O, HALICIOGLU S, et al. Feckly reduced rings[J]. Hacettepe Journal of Mathematics and Statistics, 2015, 44(2):375-384.
[11] CUI Jian, WANG Zhou. A note on strongly *-clean rings[J]. Journal of the Korean Mathematical Society, 2015, 52(4):839-851.
[12] LI Chunna, ZHOU Y. On strongly *-clean rings[J]. Journal of Algebra and Its Applications, 2011, 10(06):1363-1370.
[13] HARTE R E. On quasinilpotents in rings[J]. Panamerican Mathematical Journal, 1991, 1(1):10-16.
[14] CHEN H, HARMANCI A, OZCAN A C. Strongly J-clean rings with involutions[J]. Contemporary Mathematics, 2014(609):33-44.
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