Geodesic
The generalized Flanders' theorem in unit-regular rings
Filomat, Tome 36 (2022) no. 8, p. 2807

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DOI

Let R be a unit-regular ring, and let a, b, c ∈ R satisfy aba = aca. If ac or ba is Drazin invertible, we prove that their Drazin inverses are similar. Furthermore, if ac and ba are group invertible, then ac is similar to ba. For any n × n complex matrices A, B, C with ABA = ACA, we prove that AC and BA are similar if and only if their k-powers have the same rank. These generalize the known Flanders' theorem proved by Hartwig.
DOI : 10.2298/FIL2208807L
Classification : 15A09, 16E50, 16U90
Keywords: Flanders’ theorem, group inverse, Drazin inverse, unit-regular ring 
Dayong Liu; Aixiang Fang. The generalized Flanders' theorem in unit-regular rings. Filomat, Tome 36 (2022) no. 8, p. 2807 . doi: 10.2298/FIL2208807L
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     author = {Dayong Liu and Aixiang Fang},
     title = {The generalized {Flanders'} theorem in unit-regular rings},
     journal = {Filomat},
     pages = {2807 },
     year = {2022},
     volume = {36},
     number = {8},
     doi = {10.2298/FIL2208807L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2208807L/}
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