JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 25-30.doi: 10.6040/j.issn.1671-9352.0.2020.648

Previous Articles    

Equivalent characterization of(strong)Kasch triangular matrix ring of order n

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

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-04-13

PDF (PC)

341

Abstract: Let T be a triangular matrix ring of order n, where n≥2 is an integer. The explicit forms of maximal ideal and minimal ideal of T, and the equivalent characterizations of T being a semi-local ring and a semi-perfect ring are given. In particular, the equivalent characterizations of left Kasch and strong left Kasch triangular matrix rings of order n are given.

Key words: triangular matrix ring of order n, maximal(minimal)ideal, left Kasch ring, strong left Kasch ring

CLC Number: 

  • O153.3
[1] HERSTEIN I N. A counter example in Notherian rings[J]. Proc Nat Acad Sci, 1965, 54:1036-1037.
[2] HAGHANG A, VARADARAJAN K. Study of formal triangular matrix rings[J]. Comm Algebra, 1999, 27(11):5507-5525.
[3] HAGHANG A, VARADARAJAN K. Study of modules over formal triangular matrix rings[J]. J Pure Appl Algebra, 2000, 147:41-58.
[4] WANG Ren. Gorenstein triangular matrix rings and category algebras[J]. J Pure Appl Algebra, 2016, 220:666-682.
[5] JAIN S K, TARIQ R S. Advances in ring theory[M]. [S.l.] : Springer Science, 1997.
[6] CHEN Huanyin. On the structure of triangular matrix rings[J]. Journal of Nanjing University(Mathematical Biquarterly), 1999, 16(2):153-157.
[7] GREEN E L. On the respresentation theory of rings in matrix form[J]. Pacific J Math, 1982, 100:123-138.
[8] GOODEARL K R. Ring theory, nonsingular ring and modules[M]. [S.l.] : Marcel Dekker, 1976.
[1] 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.
[2] 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.
[3] GUO Hui-ying, ZHANG Cui-ping. Ext-strong Ding projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 31-36.
[4] ZHAO Tiao, ZHANG Chao. q-Cartan matrices of self-injective Nakayama algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 46-51.
[5] 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.
[6] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[7] 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.
[8] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[9] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[10] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[11] 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.
[12] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[13] 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.
[14] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
[15] 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.
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