Group, Moore–Penrose, core and dual core inverse in rings with involution

• Published in: Linear algebra and its applications Vol. 463; pp. 115 - 133
• Main Authors: Rakić, Dragan S., Dinčić, Nebojša Č., Djordjević, Dragan S.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.12.2014
• Subjects: [formula omitted]-Inverse; Core inverse; Core-EP generalized inverse; Dual core inverse; EP element; Group inverse; Idempotent; Inverse along an element; Moore–Penrose inverse; Ring with involution; EP element; Idempotent; Moore–Penrose inverse; Dual core inverse; Inverse along an element; Group inverse; 16U99; Core inverse; 15A09; Core-EP generalized inverse; Ring with involution; (b,c)-Inverse

Let R be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary ⁎-ring case. It is shown that the group, Moore–Penrose, core and dual core inverse are closely related and they can be treated in the same manner using appropri...