Characterizations of clean elements by means of outer inverses in rings and applications

被引：8
作者：
Mary, Xavier [1 ]
机构：
[1] Univ Paris Nanterre, ModalX, UPL, F-92000 Nanterre, France
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 07期
关键词：
Clean elements; unit-regular elements; strongly regular elements; inverses along an element; (b; c)-inverses; outer inverses; general rings; GENERALIZED INVERSES; EXTENSIONS;
D O I：
10.1142/S0219498820501340
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We characterize clean elements in unital and general rings by means of outer inverses. Some special cases, such as both clean and unit-regular elements, or strongly clean elements, are discussed. As an application, we also derive new characterizations of strongly regular elements.
引用
收藏
页数：23
相关论文
共 44 条
  • [1] Classes of Almost Clean Rings
    Akalan, Evrim
    Vas, Lia
    [J]. ALGEBRAS AND REPRESENTATION THEORY, 2013, 16 (03) : 843 - 857
  • [2] Extensions of exchange rings
    Ara, P
    [J]. JOURNAL OF ALGEBRA, 1997, 197 (02) : 409 - 423
  • [3] Azumaya G., 1954, J. Fac. Sci. Hokkaido Univ. Ser. I, V13, P34
  • [4] THE INVERSE ALONG AN ELEMENT IN RINGS
    Benitez, Julio
    Boasso, Enrico
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 : 572 - 592
  • [5] ON THE ALGEBRA OF NETWORKS
    BOTT, R
    DUFFIN, RJ
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 74 (JAN) : 99 - 109
  • [6] Continuous modules are clean
    Camillo, V. P.
    Khurana, D.
    Lam, T. Y.
    Nicholson, W. K.
    Zhou, Y.
    [J]. JOURNAL OF ALGEBRA, 2006, 304 (01) : 94 - 111
  • [7] A characterization of unit regular rings
    Camillo, VP
    Khurana, D
    [J]. COMMUNICATIONS IN ALGEBRA, 2001, 29 (05) : 2293 - 2295
  • [8] Castro-Gonzalez N., 2015, ELECTRON J LINEAR AL, V30, P8
  • [9] A question on strongly clean rings
    Chen, WX
    [J]. COMMUNICATIONS IN ALGEBRA, 2006, 34 (07) : 2347 - 2350
  • [10] Croisot R., 1953, ANN SCI ECOLE NORM S, V3, P361, DOI [10.24033/asens.1015, DOI 10.24033/ASENS.1015]
12345