JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 8-13.doi: 10.6040/j.issn.1671-9352.0.2021.055

Previous Articles    

Equivalent characterizations of strong right mininjective, semiperfect, right PF and clean triangular matrix rings of order n

TANG Guo-liang, CHEN Ling-qiao, DI Zhen-xing*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-01-07

PDF (PC)

248

Abstract: Let n be a given positive integer. The equivalent characterizations of strong right mininjective, semiperfect, right PF and clean triangular matrix rings of order n are given.

Key words: triangular matrix rings of order n, strong right mininjective rings, semiperfect rings, right PF rings, clean rings

CLC Number: 

  • O153.3
[1] HERSTEIN I N. A counter example in Noetherian rings[J]. Proc Nat Acad Sci, 1965, 54:1036-1037.
[2] HAGHANG A, VARADARAJAN K. Study of formal triangular matrix rings[J]. Comm Algrbra, 1999, 27(11):5507-5525.
[3] HAGHANG A, VARADARAJAN K. Study of modules over formal triangular matrix rings[J]. J Pure Appl Algebra, 2000, 147(1):41-58.
[4] WANG Ren. Gorenstein triangular matrix rings and category algebras[J]. J Pure Appl Algebra, 2016, 220(2):666-682.
[5] HARADA M. Self mini-injective rings[J]. Osaka Math J, 1982, 19(3):587-597.
[6] NICHOLSON W K, YOUSIF M F. Mininjective rings[J]. J Algebra, 1997, 187(2):548-578.
[7] NICHOLSON W K, YOUSIF M F. Quasi-Frobenius rings[M]. Cambridge: Cambridge University Press, 2003.
[8] DUNG B D, THOANG L D, SANH N V. When is a semiperfect ring right PF[J]. Asian-Eur J Math, 2008, 1(3):353-358.
[9] NICHOLSON W K. Lifting idempotents and exchange rings[J]. Trans Amer Math Soc, 1977, 229:269-278.
[10] MCGOVERN W W. Neat rings[J]. J Pure Appl Algebra, 2006, 205(2):243-265.
[11] ANDERSON F W, FULLER K R. Ring and categories of modules[M]. 2nd ed. New York: Springer-Verlag, 1992.
[12] NICHOLSON W K. An elementary proof of a characterization of semiperfect rings[J]. New Zealand J Math, 1996, 25(2):195-197.
[13] KASCH F. Modules and rings[M]. New York: Academic Press, 1982.
[14] NICHOLSON W K, VARADARAJAN K. Countable linear transformations are clean[J]. Proc Amer Math Soc, 1998, 126(1):61-64.
[1] ZHENG Ji-wen, CHENG Zhi. (Strongly)J-*-tripotent-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 13-19.
[2] XU Ying-ying, YIN Xiao-bin. On JGR-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 84-90.
[3] 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.
[4] 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