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

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...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 463; pp. 115 - 133
Main Authors Rakić, Dragan S., Dinčić, Nebojša Č., Djordjević, Dragan S.
Format Journal Article
LanguageEnglish
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
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Summary: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 appropriate idempotents. The several characterizations of these inverses are given. Some new properties are obtained and some known results are generalized. A number of characterizations of EP elements in R are obtained. It is shown that core and dual core inverse belong to the class of inverses along an element and to the class of (b,c)-inverses.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2014.09.003