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

Previous Articles     Next Articles

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

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.
[1] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[2] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15.
[3] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[4] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[5] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[6] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[7] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
[8] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35.
[9] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23.
[10] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.
[11] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[12] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.
[13] GAO Han-peng, YIN Xiao-bin. On strongly g(x)-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 24-29.
[14] WANG Yao, ZHOU Yun, REN Yan-li. Strongly 2-good Rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 14-18.
[15] ZHANG Zi-heng, CHU Mao-quan, YIN Xiao-bin. Some properties of GWCN rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 10-16.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!