The w -core–EP inverse in rings with involution

• Dijana Mosić ^[2] ; Huihui Zhu ^[1] ; Liyun Wu ^[1]
  1. [1] Hefei University of Technology

     Hefei University of Technology

     China

     
  2. [2] Faculty of Sciences and Mathematics, University of Niˇs, Serbia
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 2, 2024, págs. 545-565
• Idioma: inglés
• DOI: 10.33044/revuma.3478
• Enlaces
  • Texto completo
• Resumen

  • The main goal of this paper is to present two new classes of generalized inverses in order to extend the concepts of the (dual) core–EP inverse and the (dual) w-core inverse. Precisely, we introduce the w-core–EP inverse and its dual for elements of a ring with involution. We characterize the (dual) w-core–EP invertible elements and develop several representations of the w-core–EP inverse and its dual in terms of different well-known generalized inverses. Using these results, we get new characterizations and expressions for the core–EP inverse and its dual. We apply the dual w-core–EP inverse to solve certain operator equations and give their general solution forms.

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