Rings Whose Clean Elements are Uniquely Clean

被引：0
|
作者：
Calugareanu, Grigore [1 ]
Zhou, Yiqiang [2 ]
机构：
[1] Babes Bolyai Univ, Fac Math & Comp Sci, Dept Math, Cluj Napoca 400084, Romania
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NL A1C 5S7, Canada
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Idempotent; unit; clean element; uniquely clean element; abelian ring; semipotent ring; potent ring; Boolean ring; UNIT; SUM; INDEX;
D O I：
10.1007/s00009-022-02222-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The rings whose every element is uniquely clean are completely characterized in Nicholson and Zhou (Glasg Math J 46(2):227-236, 2004). These rings belong to a larger class of rings for which every clean element is uniquely clean. The latter is the topic of this article.
引用
收藏
页数：12
相关论文
共 50 条
  • [21] π-Clean and strongly π-clean rings
    Sabet, Sh. A. Safari
    Farmani, M.
    Karami, M.
    MEASUREMENT, 2017, 109 : 74 - 78
  • [22] Tripotents: a class of strongly clean elements in rings
    Calugareanu, Grigore
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2018, 26 (01): : 69 - 80
  • [23] Clean Elements in 2-Primal Rings
    Selvaraj, C.
    Petchimuthu, S.
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2011, 35 (03) : 475 - 482
  • [24] Note on Strongly Nil Clean Elements in Rings
    Aleksandra Kostić
    Zoran Z. Petrović
    Zoran S. Pucanović
    Maja Roslavcev
    Czechoslovak Mathematical Journal, 2019, 69 : 87 - 92
  • [25] Note on Strongly Nil Clean Elements in Rings
    Kostic, Aleksandra
    Petrovic, Zoran Z.
    Pucanovic, Zoran S.
    Roslavcev, Maja
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2019, 69 (01) : 87 - 92
  • [26] The Relationships Between Clean Rings, r-Clean Rings, and f-Clean Rings
    Andari, Ari
    8TH ANNUAL BASIC SCIENCE INTERNATIONAL CONFERENCE: COVERAGE OF BASIC SCIENCES TOWARD THE WORLD'S SUSTAINABILITY CHALLANGES, 2018, 2021
  • [27] Suitable elements, *-clean elements and Sylvester equations in rings with involution
    Zhu, Huihui
    Wu, Liyun
    Wang, Qing-Wen
    COMMUNICATIONS IN ALGEBRA, 2022, 50 (04) : 1535 - 1543
  • [28] *-Clean rings, some clean and almost clean Baer *-rings and von Neumann algebras
    Vas, Lia
    JOURNAL OF ALGEBRA, 2010, 324 (12) : 3388 - 3400
  • [29] On Clean Rings
    Zhang, Hongbo
    Camillo, Victor
    COMMUNICATIONS IN ALGEBRA, 2016, 44 (06) : 2475 - 2481
  • [30] On clean, weakly clean and feebly clean commutative group rings
    Li, Yuanlin
    Zhong, Qinghai
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (05)
12345