Weighted weak group inverse in a ring with involution

• Huanyin Chen ^[1]
  1. [1] Fuzhou University of International Studies and Trade, China
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 247-268
• Idioma: inglés
• DOI: 10.33044/revuma.5074
• Enlaces
  • Texto completo
• Resumen

  • We introduce the concept of the weighted weak group inverse for elements in a ring with involution. This notion naturally extends the weak group inverse for complex matrices and the weighted weak group inverse for Hilbert operators. We characterize this generalized inverse through a novel decomposition (referred to as the -group decomposition) that involves weighted group inverses and nilpotent elements. Additionally, the interrelationships among weighted weak group inverses, weighted Drazin inverses, and weighted core-EP core inverses are thoroughly investigated.

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