JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 84-90.doi: 10.6040/j.issn.1671-9352.0.2022.637

Previous Articles     Next Articles

A kind of generalization of fine rings

Yuru CUI(),Yang CHENG   

  1. College of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
  • Received:2022-11-24 Online:2024-06-20 Published:2024-06-17

RichHTML

0

PDF (PC)

282

Abstract:

A ring R is fine if every nonzero element of R is the sum of a unit and a nilpotent. We introduce the concept of J#-fine rings as a generalization of fine rings, and study basic properties of J#-fine rings and the relationship between J#-fine rings and rings which associate with J#-fine rings. We discuss the J#-fineness of matrix expansion and prove that any matrix rings over J#-fine rings are J#-fine.

Key words: fine ring, J#-fine ring, matrix ring

CLC Number: 

  • O153.3
1 NICHOLSON W K . Lifting idempotents and exchange rings[J]. Transactions of the American Mathematical Society, 1977, 229, 269- 278.
doi: 10.1090/S0002-9947-1977-0439876-2
2 DIESL A J . Nil clean rings[J]. Journal of Algebra, 2013, 383, 197- 211.
doi: 10.1016/j.jalgebra.2013.02.020
3 CUI Jian , QIN Long . Generalizations of J-clean rings[J]. Advances in Mathematics (China), 2020, 49 (1): 29- 38.
4 CǍLUGǍREANU G , LAM T Y . Fine rings: a new class of simple rings[J]. Journal of Algebra and Its Applications, 2016, 15 (9): 1650173.
doi: 10.1142/S0219498816501735
5 ZHOU Yiqiang . Generalized fine rings[J]. Journal of Algebra and Its Applications, 2022, 21 (3): 2250060.
doi: 10.1142/S0219498822500608
6 CǍLUGǍREANU G . UU rings[J]. Carpathian Journal of Mathematics, 2015, 31 (2): 157- 163.
doi: 10.37193/CJM.2015.02.02
7 VÁMOS P . 2-good rings[J]. The Quarterly Journal of Mathematics, 2005, 56 (3): 417- 430.
doi: 10.1093/qmath/hah046
8 KOȘAN M T , LEROY A , MATCZUK J . On UJ-rings[J]. Communications in Algebra, 2018, 46 (5): 2297- 2303.
doi: 10.1080/00927872.2017.1388814
[1] 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.
[2] 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.
[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] YANG Yin-yin, ZHANG Cui-ping. Gorenstein FP-injective modules over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 38-44.
[5] NIU Shao-hua, YANG Gang. n-Gorenstein projective modules over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 44-49.
[6] WU De-jun, ZHOU Hui. A characterization of Gorenstein FP-injective modules over triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 86-93.
[7] SUN Bo, YIN Yu-jie, DI Zhen-xing. Finitely embedded modules over triangular matrix rings of order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 46-53.
[8] CHEN Ling-qiao, TANG Gou-liang, DI Zhen-xing. Equivalent characterization of(strong)Kasch triangular matrix ring of order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 25-30.
[9] DI Zhen-xing, LI Xiao-man. Absolutely clean modules and Gorenstein AC flat modules over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 81-88.
[10] YANG Li-na, WANG Yao, REN Yan-li. Some new results of skew triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 49-55.
[11] ZHAO Yang, ZHANG Wen-hui. Strongly Ding projective and strongly Ding injective modules over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 37-45.
[12] MA Guang-lin, WANG Yao, REN Yan-li. Some extensions of T-nilpotent rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 68-73.
[13] ZHU Rong-min, WANG Zhan-ping. Gorenstein projective modules and dimensions over triangular matrix ring of order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 85-92.
[14] HUANG Shu-liang. Several results on derivations of formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 43-46.
[15] WANG Wen-kang. On central linear McCoy rings [J]. J4, 2013, 48(12): 6-13.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] TANG Feng-qin1, BAI Jian-ming2. The precise large deviations for a risk model with extended negatively upper orthant dependent claim  sizes[J]. J4, 2013, 48(1): 100 -106 .
[2] QANG Yao,LIU Jian and WANG Ren-qing,* . Allee effect and its significance to small population management in nature reservation and biological invasions[J]. J4, 2007, 42(1): 76 -82 .
[3] LIU Bao-cang,SHI Kai-quan . Reliablity characteristics of Srough sets[J]. J4, 2006, 41(5): 26 -29 .
[4] GUO Hui,LIN Chao . A least-squares mixed finite element procedure with the method of
characteristics for convection-dominated Sobolev equations[J]. J4, 2008, 43(9): 45 -50 .
[5] ZHANG Li,XU Yu-ming . [J]. J4, 2006, 41(5): 30 -32 .
[6] LIU Cai-ran, SONG Xian-mei. Quadratic residue codes over Fl+vFl+v2Fl[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 45 -49 .
[7] YIN Hua-jun1,2, ZHANG Xi-yong1,2*. A new method to evaluate the exponential sums of quadratic functions on finite field with character 2[J]. J4, 2013, 48(3): 24 -30 .
[8] GENG Jian-yan,YAN Jin,LI Feng . Vertex-disjoint 4-cycle in a bipartite graph[J]. J4, 2008, 43(5): 87 -92 .
[9] WANG Jin-ling,LIU Zong-cheng . The main-controlled generator[J]. J4, 2008, 43(1): 81 -87 .
[10] . Modified threestep iterative method for solving variational inequalities[J]. J4, 2009, 44(6): 69 -74 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd