Principally quasi-Baer rings

被引：149
|
作者：
Birkenmeier, GF [1 ]
Kim, JY
Park, JK
机构：
[1] Univ Louisiana, Dept Math, Lafayette, LA 70504 USA
[2] Kyung Hee Univ, Dept Math, Suwon 449701, South Korea
[3] Busan Natl Univ, Dept Math, Pusan 609735, South Korea
来源：
COMMUNICATIONS IN ALGEBRA | 2001年 / 29卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
right PP rings; Baer rings; quasi-Baer rings; biregular rings; semicentral idempotents; annihilators;
D O I：
10.1081/AGB-100001530
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We say a ring with unity is right principally quasi-Baer (or simply, right p.q. -Baer) if the right annihilator of a principal right ideal is generated las a right ideal) by an idempotent. This class of rings includes the biregular rings and is closed under direct products and Morita invariance. The 2-by-2 formal upper triangular matrix rings of this class are characterized. Connections to related classes of rings (e.g., right PP, Baer, quasi-Baer, right FPF, right GFC, etc.) are investigated. Examples to illustrate and delimit the theory are provided.
引用
收藏
页码：639 / 660
页数：22
相关论文
共 50 条
  • [1] Skew polynomial rings over σ-quasi-Baer and σ-principally quasi-Baer rings
    Han, J
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2005, 42 (01) : 53 - 63
  • [2] A note on principally quasi-Baer rings
    Liu, ZK
    COMMUNICATIONS IN ALGEBRA, 2002, 30 (08) : 3885 - 3890
  • [3] Weakly principally quasi-Baer rings
    Majidinya, A.
    Moussavi, A.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2016, 15 (01)
  • [4] ORE EXTENSIONS OF PRINCIPALLY QUASI-BAER RINGS
    Ben Yakoub, L'Moufadal
    Louzari, Mohamed
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2009, 13 (02): : 137 - 151
  • [5] PRINCIPALLY QUASI-BAER PROPERTIES OF GROUP RINGS
    Zan, Libo
    Chen, Jianlong
    STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2012, 49 (04) : 454 - 465
  • [6] A Sheaf Representation of Principally Quasi-Baer -Rings
    Khairnar, Anil
    Waphare, B. N.
    ALGEBRAS AND REPRESENTATION THEORY, 2019, 22 (01) : 79 - 97
  • [7] A NOTE ON EXTENSIONS OF PRINCIPALLY QUASI-BAER RINGS
    Cheng, Yuwen
    Huang, Feng-Kuo
    TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (07): : 1721 - 1731
  • [8] A Sheaf Representation of Principally Quasi-Baer ∗-Rings
    Anil Khairnar
    B. N. Waphare
    Algebras and Representation Theory, 2019, 22 : 79 - 97
  • [9] Prime ideals of principally quasi-Baer rings
    Birkenmeier, GF
    Kim, JY
    Park, JK
    ACTA MATHEMATICA HUNGARICA, 2003, 98 (03) : 217 - 225
  • [10] Prime ideals of principally quasi-Baer rings
    Birkenmeier G.F.
    Kim J.Y.
    Park J.K.
    Acta Mathematica Hungarica, 2002, 98 (3) : 217 - 225
12345