On partial orders in proper ∗ -rings

• Janko Marovt ^[1]
  1. [1] University of Maribor

     University of Maribor

     Eslovenia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 1, 2018, págs. 193-204
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We study orders in proper ∗-rings that are derived from the core-nilpotent decomposition. The notion of the C-N-star partial order and the S-star partial order is extended from Mn(C), the et of all n×n complex matrices, to the set of all Drazin invertible elements in proper ∗-rings with identity. Properties of these orders are investigated and their characterizations are presented. For a proper ∗-ring A with identity, it is shown that on the set of all Drazin invertible elements a∈A where the core part of a is an EP element, the C-N-star partial order implies the star partial order.