Geodesic
On idempotents of algebra of Boolean matrices
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 26-33.

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

The structure of idempotent matrices in partial semigroups of matrices of arbitrary sizes with elements from arbitrary Boolean algebra with conjunctive and disjunctive partial multiplications is investigated. The connection of solvability of the simplest matrix equations with some kind of idempotent matrices which are called “secondary idempotents” is shown. Also we show the connection of arbitrary idempotent matrices with secondary idempotents and investigate their properties. 
@article{ISU_2012_12_2_a4,
     author = {V. B. Poplavski},
     title = {On idempotents of  algebra of  {Boolean} matrices},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {26--33},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/}
}
TY  - JOUR
AU  - V. B. Poplavski
TI  - On idempotents of  algebra of  Boolean matrices
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2012
SP  - 26
EP  - 33
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/
LA  - ru
ID  - ISU_2012_12_2_a4
ER  - 
%0 Journal Article
%A V. B. Poplavski
%T On idempotents of  algebra of  Boolean matrices
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2012
%P 26-33
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/
%G ru
%F ISU_2012_12_2_a4
V. B. Poplavski. On idempotents of  algebra of  Boolean matrices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 26-33. http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/

[1] Poplavskii V. B., “O rangakh, klassakh Grina i teorii opredelitelei bulevykh matrits”, Diskretnaya matematika, 20:4 (2008), 42–60 | DOI | MR | Zbl

[2] Bisli L. B., Guterman A. E., Kang K.-T., Song S.-Z., “Idempotentnye matritsy i mazhorirovanie”, Fundamentalnaya i prikladnaya matematika, 13:1 (2007), 11–29 | MR | Zbl

[3] Kumarov V. B., “Reshetka idempotentnykh matrits nad distributivnymi reshetkami”, Fundamentalnaya i prikladnaya matematika, 13:4 (2007), 121–144 | MR | Zbl

[4] Luce R. D., “A note on Boolean matrix theory”, Proc. Am. Math. Soc., 3 (1952), 382–388 | DOI | MR | Zbl

[5] Rudeanu S., Boolean functions and equations, North-Holland Publishing Company, Amsterdam–London; American Elsevier Publishing Company, Inc., N.Y., 1974, 442 pp. | MR | Zbl

[6] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, v 2 t., v. 1, Mir, M., 1972, 287 pp. | Zbl