Geodesic
Jacobson's lemma and Cline's formula for weighted generalized inverses in a ring with involution
Filomat, Tome 37 (2023) no. 16, p. 5313

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DOI

Let R be a ring with involution and e, f ∈ R be Hermitian and invertible. We first present some equivalent conditions for paq to be {1, 3 f }-invertible, assuming that p, a, q ∈ R with p ′ pa = a = aqq ′ for some p ′ , q ′ ∈ R and a is {1, 3e}-invertible. Then, these results are applied to give the sufficient and necessary conditions under which Jacobson's lemma and Cline's formula for weighted pseudo core inverses hold. Also, Jacobson's lemma for weighted Moore-Penrose inverses is investigated.
DOI : 10.2298/FIL2316313Z
Classification : 16U90, 15A09
Keywords: Cline’s formula, Jacobson’s lemma, Weighted pseudo core inverse, Weighted Moore-Penrose inverse 
Yukun Zhou; Jianlong Chen. Jacobson's lemma and Cline's formula for weighted generalized inverses in a ring with involution. Filomat, Tome 37 (2023) no. 16, p. 5313 . doi: 10.2298/FIL2316313Z
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     title = {Jacobson's lemma and {Cline's} formula for weighted generalized inverses in a ring with involution},
     journal = {Filomat},
     pages = {5313 },
     year = {2023},
     volume = {37},
     number = {16},
     doi = {10.2298/FIL2316313Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2316313Z/}
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