Geodesic
On the Ranks of Idempotent Matrices over Skew Semifields
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 832-839

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As is well known, every positive idempotent matrix is of rank 1. It is proved that idempotent matrices without zeros have this property over many skew semifields, and all these skew semifields are described.
Mots-clés : idempotent matrix
Keywords: rank, skew semifield, (weakly) additively idempotent skew semifield, (weakly) additively cancellable skew semifield. 
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     author = {S. N. Il'in},
     title = {On the {Ranks} of {Idempotent} {Matrices} over {Skew} {Semifields}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {832--839},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a3/}
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S. N. Il'in. On the Ranks of Idempotent Matrices over Skew Semifields. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 832-839. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a3/