JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 20-27.doi: 10.6040/j.issn.1671-9352.0.2019.440

Previous Articles     Next Articles

Strongly g(x)-J#-clean rings

LIU Song-song, WU Jun*   

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

PDF (PC)

494

Abstract: The concept of strongly g(x)-J#-clean rings are introduced. Some properties of strongly g(x)-J#-cleanrings are obtained. Moreover, equivalent characterizations of strongly J#-cleanrings are given by means of strongly g(x)-J#-clean rings.

Key words: strongly J-cleanring, strongly J#-cleanring, strongly g(x)-J-cleanring, strongly g(x)-J#-cleanring

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. Strongly clean rings and Fittings lemma[J]. Communications in Algebra, 1999, 27(8):3583-3592.
[3] CAMILLO V P, SIMóN J J. The Nicholson-Varadarajan theorem on clean linear transformations[J]. Glasgow Mathematical Journal, 2002, 44(3):365-369.
[4] CHEN Huanyin. On strongly J-clean rings[J]. Communications in Algebra, 2010, 38(10):3791-3804.
[5] JAVADI H S, JAMSHIDVAND S, MALEKI M. On strongly J-clean rings associated with polynomial identity g(x)=0[J]. Journal of Linear and Topological Algebra, 2013, 2(2):71-76.
[6] 程瑶,刘少然,殷晓斌.强J-clean环的推广[J].安徽师范大学学报(自然科学版),2017,40(4):323-326. CHENG Yao, LIU Shaoran, YIN Xiaobin. The generalization of strongly J-clean rings[J]. Journal of Anhui Normal University(Natural Science), 2017, 40(4):323-326.
[7] FAN Lingling, YANG Xiande. On rings whose elements are the sum of a unit and a root of a fixed ploynomial[J]. Communications in Algebra, 2008, 36(1):269-278.
[8] XIAO Guangshi, TONG Wenting. n-clean rings and weakly unit stable range rings[J]. Communications in Algebra, 2005, 33(5):1501-1517.
[9] HANI A K, HANDAM A H. On weakly g(x)-nil clean rings[J]. International Journal of Pure and Applied Mathematics, 2017, 114(2):191-202.
[10] ASHRAFI N, AHMADI Z. Weakly g(x)-clean rings[J].Iranian Journal of Mathematical Sciences and Informatics, 2012, 7(2):83-91.
[11] HANDAM A H, KHASHAN H A. Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute[J].Open Mathematics, 2017, 15(1):420-426.
[1] Yuru CUI,Yang CHENG. A kind of generalization of fine rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 84-90.
[2] Jie WANG,Wenjing CHEN. On w-FPn-projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 64-70.
[3] Wenjing CHEN,Wen GAO. Gorenstein FP-injective modules over Morita rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 9-15.
[4] Liu ZHOU,Lei QIAO,Dan ZHAO. On w-IFP-flat modules and w-IFP-injective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 22-31.
[5] Dong SU. The module algebra structures of dihedral groups on the full matrix algebra of 2×2 [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 14-21, 31.
[6] Cuiping ZHANG,Jiaojiao DONG,Yinyin YANG. Gorenstein FP-injective dimensions over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 8-13.
[7] Yao WANG,Xin LI,Yanli REN. *-zip rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 1-7.
[8] Hua SUN,Jian ZOU,Ruju ZHAO. Automorphism group of Green algebra of 8-dimensional Radford Hopf algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(11): 61-70.
[9] Longjiao YANG,Hailou YAO. Gorenstein weak projective comodules over a coalgebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 43-47, 56.
[10] Cuiping ZHANG,Wenfei ZHANG,Fuxia YANG. $\mathscr{X}$-strongly n-Gorenstein projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 26-32, 42.
[11] Xianhong YANG,Guoliang TANG,Zhenxing DI. Recollements of Gorenstein flat cotorsion modules over triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 18-25.
[12] Mengge GUAN,Hainan ZHOU,Junchao WEI. Some equivalent characterizations on EP elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 13-17.
[13] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[14] YIN Jun-qi, YANG Gang. Gorenstein DG-injective complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 28-33.
[15] ZHANG Cui-ping, LIU Ya-juan. Strongly Gorenstein C-injective module and strongly Gorenstein C-flat module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 24-30.
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