Journal of East China Normal University(Natural Science) >

2024 , Vol. 2024 >Issue 2: 30 - 32

DOI: https://doi.org/10.3969/j.issn.1000-5641.2024.02.004

Mathematics

On *r-clean rings

  • Jian QIN ,
  • Zhiling YING ,
  • Hua ZHOU
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  • 1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing　210023, China

Received date: 2023-03-21

  Online published: 2024-03-18

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Abstract

An involution ring is called a *r-clean ring if every element is the sum of a projection and a *-regular element. Some extensions of *r-clean rings are discussed, and a characterization of the element in a *-abelian *r-clean ring is given.

Key words： *r-clean ring; *-clean ring; *-regular ring

Cite this article

Jian QIN , Zhiling YING , Hua ZHOU . On *r-clean rings[J]. Journal of East China Normal University(Natural Science), 2024 , 2024(2) : 30 -32 . DOI: 10.3969/j.issn.1000-5641.2024.02.004

References

1 NICHOLSON W K.. Lifting idempotents and exchange rings. Transactions of the American Mathematical Society, 1977, 229, 269- 278.
2 BERBERIAN S K. Baer *-Rings [M]. New York: Springer Verlag, 1972.
3 VA? L.. *-Clean rings; some clean and almost clean Baer *-rings and von Neumann algebras. Journal of Algebra, 2010, 324 (12): 3388- 3400.
4 LI C N, ZHOU Y Q.. On strongly *-clean rings. Journal of Pure and Applied Algebra, 2011, 10 (6): 1363- 1370.
5 CHEN J L, CUI J.. Two questions of L.Va? on *-clean rings. Bulletin of the Australian Mathematical Society, 2012, 88, 499- 505.
6 CUI J, YIN X B.. Some characterizations of *-regular rings. Communications in Algebra, 2017, 45 (2): 841- 848.
7 CUI J, YIN X B.. A question on *-regular rings. Bulletin of the Korean Mathematical Society, 2018, 55 (5): 1333- 1388.
8 王菲. *-正则局部环和*-UR环的研究 [D]. 南京: 南京邮电大学理学院, 2020.
9 KOLIHA J J, DJORDJEVIC D, CVETKOVIC D.. Moore-Penrose inverse in rings with involution. Linear Algebra and its Applications, 2007, 426, 371- 381.
10 HANDELMAN D.. Perspectivity and cancellation in regular rings. Journal of Algebra, 1977, 48, 1- 16.
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