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Characterizations and Representations of Core and Dual Core Inverses

  Published:2016-08-17
 Printed: Jun 2017
  • Jianlong Chen,
    Department of Mathematics, Southeast University, Nanjing 210096, China
  • Huihui Zhu,
    Department of Mathematics, Southeast University, Nanjing 210096, China
  • Pedro Patricio,
    Departamento de Matemática e Aplicações, Universidade do Minho, Braga 4710-057, Portugal
  • Yulin Zhang,
    Departamento de Matemática e Aplicações, Universidade do Minho, Braga 4710-057, Portugal
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Abstract

In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.
Keywords: regularities, group inverses, Moore-Penrose inverses, core inverses, dual core inverses, Dedekind-finite rings regularities, group inverses, Moore-Penrose inverses, core inverses, dual core inverses, Dedekind-finite rings
MSC Classifications: 15A09, 15A23 show english descriptions Matrix inversion, generalized inverses
Factorization of matrices
15A09 - Matrix inversion, generalized inverses
15A23 - Factorization of matrices
 

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