JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 14-22.doi: 10.6040/j.issn.1671-9352.0.2021.324

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2-nil-clean rings

CHEN Jiang-huan1, WANG Yao1, REN Yan-li2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2022-01-07

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Abstract: The concept of 2-nil-clean rings is introduced. A ring R is called 2-nil-clean if every element in R is the sum of an idempotent and two nilpotents. Making use of the classical methods in ring theory, it is investigated that some properties of them and the relationship between 2-nil-clean rings and related rings.

Key words: clean rings, 2-nil-clean rings, ring extension

CLC Number: 

  • O153.3
[1] WANG Zhou, CHEN Jianlong. 2-clean rings[J]. Canad Math Bull, 2006, 52(1):145-153.
[2] DIESL A J. Nil clean rings[J]. J Algebra, 2013, 383:197-211.
[3] KO??塁AN T, WANG Z, ZHOU Y. Nil-clean and strongly nil-clean rings[J]. J Pure Appl Algebra, 2016, 220(2):633-646.
[4] CHEN Huanyin, SHEIBANI M. Strongly weakly nil-clean rings[J]. J Algebra Appl, 2017, 16(12):1-12.
[5] CHEN Huanyin, SHEIBANI M. Strongly 2-nil-clean rings[J]. J Algebra Appl, 2017, 16(9):1-12.
[6] ANDRICA D, CĂLUGĂREANU G. A nil-clean 2×2 matrix over the integers which is not clean[J]. J Algebra Appl, 2014, 13(6):1-9.
[7] CĂLUGĂREANU G. UU rings[J]. Carpathian J Math, 2015, 31(2):157-163.
[8] DANCHEV P V. Weakly invo-clean unital rings[J]. Afr Mat, 2017, 28(7):1285-1295.
[9] YING Zhiling, CHEN Jianlong. On UR-rings[J]. J Math Res Expos, 2009, 29(2):355-361.
[10] KARPARVAR A M, AMINI B, AMINI A, et al. Soclean rings[J]. Bull Iranian Math Soc, 2019, 45(4):1071-1089.
[11] CHEN Huanyin, GURGUN O, HALICIOGLU S, et al. Rings in which nilpotents belong to Jacobson radical[J]. An ??塁tiin??塅 Univ Al I Cuza Ia??塂i Mat(N.S.), 2016, 62(2):595-606.
[12] 王尧, 周昊, 任艳丽. 环R{D,C}的一些性质[J]. 数学的实践与认识, 2020(12):173-181. WANG Yao, ZHOU Hao, REN Yanli. Some properties of ring R{D,C}[J]. Mathematics in Practice and Theory, 2020(12):173-181.
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