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    

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)

294

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] WANG Zhan-ping, YUAN Kai-ying. Strongly Gorenstein injective modules with respect to a cotorsion pair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 102-107.
[2] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[3] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15.
[4] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[5] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[6] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[7] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[8] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[9] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23.
[10] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
[11] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35.
[12] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.
[13] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[14] WANG Yao, ZHOU Yun, REN Yan-li. Strongly 2-good Rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 14-18.
[15] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.
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