JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (12): 63-68.doi: 10.6040/j.issn.1671-9352.0.2020.233

Previous Articles    

General symmetric rings

QIN Lan-lan1, 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:2020-12-01

PDF (PC)

371

Abstract: In the general ring(not necessarily with 1)category, the concepts of left and right symmetric rings are different. The concept of general symmetric rings in general ring category is introduced and give its characterization, discuss the relationship between general symmetric rings and related rings as well as their ring extensions.

Key words: general symmetric ring, right symmetric ring, Baer ring, p.p.-ring

CLC Number: 

  • O153.3
[1] SHAFEE B H, NAUMAN S K. On extensions of right symmetric rings without identity[J]. Adv Pure Math, 2014, 4(12):665-673.
[2] LAMBEK J. On the representation of modules by sheaves of modules of quotients[J]. Ring Theory, 1972: 231-234.
[3] ANDERSON D D, CAMILLO V. Semigroups and rings whose zero products commute[J]. Comm Algebra, 1999, 27(6):2847-2852.
[4] MARKS G. Reversible and symmetric rings[J]. J Pure Appl Algebra, 2002, 174(3):311-318.
[5] 李晓伟,任艳丽. 右对称环[J]. 数学理论与应用,2012,32(2):33-38. LI Xiaowei, REN Yanli. Right symmetric rings[J]. Math Theory Appl, 2012, 32(2):33-38.
[6] WANG Zhanping. Extensions of symmetric rings[J]. J Math Res Exp, 2007, 27(2):229-235.
[7] HUH C, KIM H K, KIM N K, et al. Basic examples and extensions of symmetric rings[J]. J Pure Appl Algebra, 2005, 202(1-3):154-167.
[8] ANTOINE R. Nilpotent elements and Armendariz rings[J]. J Algebra, 2008, 319(8):3128-3140.
[9] OUYANG Lunqun, CHEN Huanyin. On weak symmetric rings[J]. Comm Algebra, 2010, 38(2):697-713.
[10] KIM N K, YANG L. Extensions of reversible rings[J]. J Pure Appl Algebra, 2003, 185(1):207-223.
[11] ANDERSON D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998, 26(7):2265-2272.
[12] 宿维军. 广义可逆环[J]. 北京师范大学学报(自然科学版),2011,47(1):17-22. SU Weijun. Generalized reversible rings[J]. J Beijing Normal University(Natural Science), 2011, 47(1):17-22.
[13] KIM N K, LEE K H, LEE Y. Power series rings satisfying a zero divisor property[J]. Comm Algebra, 2006, 34(6):2205-2218.
[1] GENG Dao-hong, WANG Yao, REN Yan-li. α-skew Armendariz rings relative to a monoid [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 1-5.
[2] WANG Yao, ZHANG Jiu-lin, REN Yan-li. On Ore extensions of nilpotent p.p.-rings and nilpotent Baer rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 76-81.
[3] 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.
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