Geodesic
On Commuting Generalized Inverses in Semigroups
Publications de l'Institut Mathématique, _N_S_65 (1999) no. 79, p. 103 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $S$ be a semigroup and let $a\in S$. In this note we describe all possible commuting generalized inverses of $a$ (in the sense of Definitions 1 and 2). It turns out that the Drazin inverse of $a$ is the only generalized inverse of $a$ which commutes with $a$.
Classification : 20M05 
@article{PIM_1999_N_S_65_79_a9,
     author = {Jovan D. Ke\v{c}ki\'c and Svetozar Mili\'c},
     title = {On {Commuting} {Generalized} {Inverses} in {Semigroups}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {103 },
     publisher = {mathdoc},
     volume = {_N_S_65},
     number = {79},
     year = {1999},
     zbl = {1011.20052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1999_N_S_65_79_a9/}
}
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Jovan D. Kečkić; Svetozar Milić. On Commuting Generalized Inverses in Semigroups. Publications de l'Institut Mathématique, _N_S_65 (1999) no. 79, p. 103 . http://geodesic.mathdoc.fr/item/PIM_1999_N_S_65_79_a9/