JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 68-73.doi: 10.6040/j.issn.1671-9352.0.2019.135

Previous Articles    

Some extensions of T-nilpotent rings

MA Guang-lin1, WANG Yao1, REN Yan-li2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2019-12-11

PDF (PC)

321

Abstract: Some extension properties of T-nilpotent rings are investigated. It is mainly proved that(1)If R is a ring and α an automorphism of R, then R is a left T-nilpotent ring if and only if the skew polynomial ring R［x;α］ over R is a left T-nilpotent ring, if and only if the skew Laurent polynomial ring R［x,x-1;α］ is a left T-nilpotent ring;(2)R is a left T-nilpotent ring if and only if the Nagata extension over R is a left T-nilpotent ring, if and only if the skew triangular matrix ring over R is a left T-nilpotent ring.

Key words: T-nilpotent ring, skew polynomial ring, skew Laurent polynomial ring, Nagata extension, skew triangular matrix ring

CLC Number: 

  • O153.3
[1] LEVITZKI J. Contributions to the theory of nil rings[J]. Riveon Lematematika, 1953, 7(1):50-70.
[2] BASS H. Finitistic dimension and a homological generalization of semi-primary rings[J]. Trans Amer Math Soc, 1960, 95(3):466-488.
[3] SANDS A D. On M-nilpotent rings[J]. Proc Roy Soc Ediburgh, 1982, 93(1-2): 63-70.
[4] BJÖRK J E. Rings satisfying a minimum condition on principal ideals[J]. J Reine Angew Math, 1969, 236(2):112-119.
[5] 王俊民. T-幂零环与Baer根[J]. 云南大学学报(自然科学版), 1991, 13(2):105-108. WANG Junmin. On T-nilpotent rings and Baer radical[J]. Journal of Yunnan University(Natural Science), 1991, 13(2):105-108.
[6] GARDNER B J, KELAREV A V. Two generalizations of T-nilpotence[J]. Algebra Colloq, 1998, 5(4):449-458.
[7] DU X K. Left T-idempotence and left T-stability of semigroup rings[J]. Comm Algebra, 2001, 29(12):5477-5497.
[8] 王尧,任艳丽. Morita context环的T-幂零性和周期性[J]. 数学杂志,2008,28(6):689-695. WANG Yao, REN Yanli. T-niplotency and periodicity for Morita cotext rings[J]. J of Math, 2008, 28(6):689-695.
[9] GARDNER B J. Some aspects of T-nilpotence[J]. Pacific J Math, 1974, 53(1):117-130.
[10] 侯国荣. 关于环的T-幂零性[J]. 天津师大学报(自然科学版),1985,10(1):38-41. HOU Guorong. On T-niplotency of rings[J]. Journal of Tianjin Normal University(Natural Science Edition), 1985, 10(1):38-41.
[11] ANDERSON D D, CAMILLO V. Semigroups and rings whose zero products commute[J]. Comm Algebra, 1999, 27(6):2847-2852.
[12] JORDAN D A. Bijective extensions of injective ring endomorphisms[J]. J London Math Soc, 1982, 25(2):435-448.
[13] NAGATA M. Local rings[M]. New York: Interscience, 1962.
[14] NASR-ISFAHANI A R. On skew triangular matrix rings[J]. Comm Algebra, 2011, 39(11):4461-4469.
[15] 刘绍学. 环与代数[M]. 北京:科学出版社,1983. LIU Shaoxue. Rings and algebra[M]. Beijing: Science Press, 1983.
[1] WANG Yao1, JIANG Mei-mei1, REN Yan-li2*. Some properties of skew polynomial rings#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 40-45.
[2] ZHANG Wan-ru. Skew nil McCoy rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 57-62.
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