Geodesic
Further results on the EP-ness and co-EP-ness involving Mary inverses
Filomat, Tome 37 (2023) no. 30, p. 10237

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DOI

Let R be a ring and a, d 1 , d 2 ∈ R. First, we obtain several equivalent conditions for the equality aa ∥d 1 = a ∥d 2 a to hold, under the condition a ∈ R ∥d 1 ∩ R ∥d 2. Then, when a ∈ R ∥ • d 1 ∩ R ∥ • d 2 , the equality a m a ∥d 1 = a ∥d 2 a m (m ∈ N) is also investigated by means of Drazin inverses. Next, some characterizations for the invertibility of aa ∥d 1 − a ∥d 2 a are obtained. Particularly, a number of examples are given to illustrate our results.
DOI : 10.2298/FIL2330237Z
Classification : 15A09, 16W10, 16N20, 16B99
Keywords: Ring, Invertibility, Inverse along an element, Co-EP elements, EP elements 
Honglin Zou; Yuedi Zeng; Nan Zhou; Sanzhang Xu. Further results on the EP-ness and co-EP-ness involving Mary inverses. Filomat, Tome 37 (2023) no. 30, p. 10237 . doi: 10.2298/FIL2330237Z
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     title = {Further results on the {EP-ness} and {co-EP-ness} involving {Mary} inverses},
     journal = {Filomat},
     pages = {10237 },
     year = {2023},
     volume = {37},
     number = {30},
     doi = {10.2298/FIL2330237Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2330237Z/}
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