JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 1-10.doi: 10.6040/j.issn.1671-9352.0.2023.198

    Next Articles

Srongly 2-idem-J-clean rings

WANG Yao1, CHEN Jianghuan2, REN Yanli3*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Computer and Information Engineering, Nantong Institute of Technology, Nantong 226001, Jiangsu, China;
    3. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2024-12-12

PDF (PC)

157

Abstract: In this paper, we introduce the concept of strongly 2-idem-J-clean rings. A ring R is called a strong 2-idempotent J-clean ring, if for any a∈R there exists e, f∈Id(R), j∈J(R) such that a=e+f+j, and any two of e, f, j satisfy multiplicative commutativity. Their basic properties and the relation between them and related rings are given to further enrich the theory of clean rings.

Key words: clean ring, J-clean ring, strongly 2 idem-J-clean ring

CLC Number: 

  • O153.3
[1] WANG Z, CHEN J L. 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?瘙塁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 H Y, SHEIBANI M. Strongly weakly Nil-clean rings[J]. J Algebra Appl, 2017, 16(12):1-12.
[5] CHEN H Y, SHEIBANI M. Strongly 2-Nil-clean rings[J]. J Algebra Appl, 2017, 16(9):1-12.
[6] CHEN H Y, GURGUN O, HALICIOGLU S, et al. Rings in which nilpotents belong to Jacobson radical[J]. An ?瘙塁tiin?瘙塅 Univ Al I Cuza din Ia?瘙塂i Mat(N.S.), 2016, 62(2):595-606.
[7] MA G L, WANG Y, REN Y L. On rings whose Jacobson radical coincides with upper nilradical[J]. Turk J Math, 2021, 45(1):782-796.
[8] JIANG M M, WANG Y, REN Y L. Extensions and topological conditions of NJ rings[J]. Turk J Math, 2019, 43(1):44-62.
[9] 唐高华,臧乃策,赵汝菊. 强J-quasi-clean环[J]. 南宁师范大学学报(自然科学版),2023,40(1):1-6. TANG Gaohua, ZANG Naice, ZHAO Ruju. Strongly J-quasi-clean rings[J]. Journal of Nanning Normal University(Natural Science Edition), 2023, 40(1):1-6.
[10] HEGDE S. On uniquely clean elements[J]. Comm Algebra, 2023, 51(5):1835-1839.
[11] BARATI R, MOUSSAVI A. A note on weakly Nil-clean rings[J]. Mediterr J Math, 2023, 20(2):9-23.
[12] ZHOU Y Q. Two questions on semi-clean group rings[J]. J Pure Appl Algebra, 2022, 226(11):107-116.
[13] GORMAN A B, DIESL A. Ideally Nil clean rings[J]. Comm Algebra, 2021, 49(11):4788-4799.
[14] CHEN H Y. On strongly J-clean rings[J]. Comm Algebra, 2010, 38(10):3790-3804.
[15] YING Z L, KO?瘙塁AN T. Rings in which every element is a sum of two tripotents[J]. Canad Math Bull, 2016, 59(3):661-672.
[16] ZHOU Y Q. Rings in which elements are sums of nilpotents, idempotents and tripotents[J]. J Algebra Appl, 2018, 17(1):1-7.
[17] LAM T Y. A first course in noncommutative rings[M]. New York: Springer, 1991.
[18] YU H P. On quasi-duo rings[J]. Glasgow Math J, 1995, 37(1):21-31.
[19] THIERRIN G. On duo rings[M]. 2nd ed. New York: Springer, 2001.
[20] KEE K H, KYUN K N, YANG L. Weakly duo rings with Nil Jacobson radical[J]. J Korean Math Soc, 2005, 42(3):457-470.
[21] NICHOLSON W K. Lifting idempotents and exchange rings[J]. Trans Amer Math Soc, 1977, 229(5):269-278.
[22] ABDOLYOUSEFI M S, CHEN H Y. Rings in which elements are sums of tripotents and nilpotents[J]. J Algebra Appl, 2018, 17(3):1-11.
[23] CUI J, YIN X B. Rings with 2-UJ property[J]. Comm Algebra, 2020, 48(4):1382-1391.
[24] BEDI S S,RAM J. Jacobson radical of skew polynomial rings and skew group rings[J]. Israel J Math, 1980, 35(4):327-338.
[25] HONG C Y, KWAK T K, RIZVI S T. Extensions of generalized Armendariz rings[J]. Algebra Colloq, 2006, 13(2):253-266.
[26] NASR-ISFAHANI A R, MOUSSAVI A. A generalization of reduced rings[J]. J Algebra Appl, 2012, 11(4):1-30.
[27] 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]. Math Prac Theory, 2020(12):173-181.
[1] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[2] CHEN Jiang-huan, WANG Yao, REN Yan-li. 2-nil-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 14-22.
[3] TANG Guo-liang, CHEN Ling-qiao, DI Zhen-xing. Equivalent characterizations of strong right mininjective, semiperfect, right PF and clean triangular matrix rings of order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 8-13.
[4] ZHENG Ji-wen, CHENG Zhi. (Strongly)J-*-tripotent-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 13-19.
[5] SUN Xiao-qing, XIAO Yan-ting, CUI ran-ran. Discussions on the Q-cleanness of rings and Q-clean corner [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 79-83.
[6] XU Ying-ying, YIN Xiao-bin. On JGR-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 84-90.
[7] CHEN Yi-ning, QIN Long. Strongly g(x)-nil-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 41-46.
[8] 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.
[9] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[10] 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.
[11] WANG Xiu-lan. Semiboolean group rings [J]. J4, 2012, 47(10): 18-20.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd