Open AccessRank equalities related to a class of outer generalized inverse
Author(s) -
Jianlong Chen,
Shaoyuan Xu,
Julio Benítez,
Xiaofeng Chen
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1917611c
Subject(s) - mathematics , rank (graph theory) , inverse , aka , drazin inverse , combinatorics , moore–penrose pseudoinverse , class (philosophy) , generalized inverse , ring (chemistry) , geometry , chemistry , organic chemistry , artificial intelligence , library science , computer science
In 2012, Drazin introduced a class of outer generalized inverse in a ring R, the (b,c)-inverse of a for a, b, c ? R and denoted by a||(b,c). In this paper, rank equalities of AkA||(B,C)- A||(B,C)Ak and (A*)kA||(B,C)-A||(B,C)(A*)k are obtained. As applications, weinvestigate equivalent conditions for the equalities (A*)kA||(B,C) = A||(B,C)(A*)k and AkA||(B,C) = A||(B,C)Ak. As corollaries we obtain rank equalities related to the Moore-Penrose inverse, the core inverse, and the Drazin inverse. The paper finishes with some rank equalities involving different e