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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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/
@article{MZM_2012_91_6_a3,
     author = {S. N. Il'in},
     title = {On the {Ranks} of {Idempotent} {Matrices} over {Skew} {Semifields}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {832--839},
     year = {2012},
     volume = {91},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a3/}
}
TY  - JOUR
AU  - S. N. Il'in
TI  - On the Ranks of Idempotent Matrices over Skew Semifields
JO  - Matematičeskie zametki
PY  - 2012
SP  - 832
EP  - 839
VL  - 91
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a3/
LA  - ru
ID  - MZM_2012_91_6_a3
ER  - 
%0 Journal Article
%A S. N. Il'in
%T On the Ranks of Idempotent Matrices over Skew Semifields
%J Matematičeskie zametki
%D 2012
%P 832-839
%V 91
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a3/
%G ru
%F MZM_2012_91_6_a3

[1] J. S. Golan, Semirings and Their Applications, Kluwer Acad. Publ., Dordrecht, 1999 | MR | Zbl

[2] J. S. Golan, Semirings and Affine Equations over Them. Theory and Applications, Math. Appl., 556, Kluwer Acad. Publ., Dordrecht, 2003 | MR | Zbl

[3] D. Dolžan, P. Oblak, “Idempotent matrices over antirings”, Linear Algebra Appl., 431:5-7 (2009), 823–832 | DOI | MR | Zbl

[4] L. B. Bisli, A. E. Guterman, K. Kang, S. Song, “Idempotentnye matritsy i mazhorirovanie”, Fundament. i prikl. matem., 13:1 (2007), 11–29 | MR | Zbl

[5] K.-T. Kang, S.-Z. Song, Y.-O. Yang, “Characterizations of fuzzy idempotent matrices”, J. Fuzzy Math., 16:3 (2008), 653–663 | MR | Zbl

[6] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 | MR | Zbl

[7] A. E. Guterman, “Rank and determinant functions for matrices over semirings”, Surveys in Contemporary Mathematics, London Math. Soc. Lecture Note Ser., 347, Cambridge Univ. Press, Cambridge, 2008, 1–33 | MR | Zbl