JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 13-19.doi: 10.6040/j.issn.1671-9352.0.2019.436

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(Strongly)J-*-tripotent-clean rings

ZHENG Ji-wen, CHENG Zhi*   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003, Anhui, China
  • Published:2020-07-14

Abstract: The concept of(strongly)J-*-tripotent-clean ring is introduced. An example is given to illustrate that strongly J-*-tripotent-clean ring is a proper subclass of strongly clean ring. Some equivalent definitions of strongly J-*-tripotent-clean ring are given. As an application, some corresponding properties for transformations of rings are also given.

Key words: strongly *-clean rings, (strongly)J-*-tripotent-clean rings, *-tripotent, Abelian rings

CLC Number: 

  • O153.3
[1] NICHOLON W K. Lifting idempotents and exchange rings[J]. Transactions of the American Mathematical Society, 1977, 229:269-278.
[2] CHEN Huanyin, HARMANCI A, OZCAN A C. Strongly J-clean rings with involutions[J]. Contemp Math, 2014, 609:33-44.
[3] NICHOLON W K. Strongly clean rings and Fittings lemma[J]. Communications in Algebra, 1999, 27(8):3583-3592.
[4] CHEN Huanyin. On strongly J-clean rings[J]. Communications in Algebra, 2010, 38(10):3790-3804.
[5] VAS L. *-Clean rings; some clean and almost clean Baer *-rings and von Neumann algebras[J]. Journal of Algebra, 2010, 324(12):3388-3400.
[6] LI Chunna, ZHOU Yiqiang. On strongly *-clean rings[J]. Journal of Algebra and Its Applications, 2011, 10(6):1363-1370.
[7] CHEN Huanyin, ABDOLYOUSELFI M S. Strongly 2-nil-clean rings with involutions[J]. Czechoslovak Mathematical Journal, 2019, 69(2):317-330.
[8] CHEN Huanyin, SHEIBANI M. Strongly 2-nil-clean rings[J]. Journal of Algebra and Its Applications, 2017, 16(9):1750178.
[9] DIESL A J. Nil clean rings[J]. Journal of Algebra, 2013, 383:197-211.
[10] DANCHEV P V. Feebly J-clean unital rings[J]. International Journal of Algebra, 2017, 11(6):287-290.
[11] DANCHEV P V. Invo-clean unital rings[J]. Communications of the Korean Mathematical Society, 2017, 32(1):19-27.
[12] KOSAN M T, YILDIRIM T, ZHOU Yiqiang. Rings whose elements are the sum of a tripotent and an element from the Jacobson radical[J]. Canadian Mathematical Bulletin, 2019, 62(4):810-821.
[1] YIN Xiao-bin1, HUANG Xiao-lin1, WANG Kai-yun2. Endomorphism rings of quasi AP-injective modules [J]. J4, 2010, 45(6): 31-34.
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