Prime lattice matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 167-179.

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

We consider properties of prime lattice matrices over the following lattices: chains, direct sums of chains, Boolean lattices.
@article{FPM_2012_17_4_a9,
     author = {V. E. Marenich},
     title = {Prime lattice matrices},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {167--179},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a9/}
}
TY  - JOUR
AU  - V. E. Marenich
TI  - Prime lattice matrices
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2012
SP  - 167
EP  - 179
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a9/
LA  - ru
ID  - FPM_2012_17_4_a9
ER  - 
%0 Journal Article
%A V. E. Marenich
%T Prime lattice matrices
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 167-179
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a9/
%G ru
%F FPM_2012_17_4_a9
V. E. Marenich. Prime lattice matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 167-179. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a9/

[1] Devadze Kh. M., “Porozhdayuschie mnozhestva polugruppy vsekh binarnykh otnoshenii v konechnom mnozhestve”, Dokl. AN BSSR, 12:9 (1968), 765–768 | MR | Zbl

[2] Marenich V. E., “Prostye matritsy nad distributivnymi reshëtkami”, Fundament. i prikl. mat., 14:7 (2008), 157–173 | MR

[3] Sachkov V. N., Tarakanov V. E., Kombinatorika neotritsatelnykh matrits, TVP, M., 2000 | MR | Zbl

[4] Skornyakov L. A., “Obratimye matritsy nad distributivnymi strukturami”, Sib. mat. zhurn., 27:2 (1986), 182–185 | MR | Zbl

[5] Borosh J., Hartfiel D. J., Maxson C. J., “Answers to questions posed by Richman and Schneider”, Linear and Multilinear Algebra, 3 (1976), 255–258 | DOI | MR | Zbl

[6] De Caen D., Prime Boolean matrices, M. Sci. Thesis, Queen's Univ., Kingston, Ontario, 1979

[7] De Caen D., Gregory D. A., “Prime Boolean matrices”, Combinatorial Mathematics VII, Proc. 7th Aust. Conf. (Newcastle, 1979), Lect. Notes Math., 829, Springer, Berlin, 1980, 76–82 | DOI | MR

[8] De Caen D., Gregory D. A., “Primes in the semigroup of Boolean matrices”, Linear Algebra Appl., 37 (1981), 119–134 | DOI | MR | Zbl

[9] Cho H. H., “Prime Boolean matrices and factorizations”, Linear Algebra Appl., 190 (1993), 87–98 | DOI | MR | Zbl

[10] Cho H. H., “Permanents of prime Boolean matrices”, Bull. Korean Math. Soc., 35:3 (1998), 605–613 | MR | Zbl

[11] Giveon J., “Lattice matrices”, Inform. Control., 7 (1964), 477–484 | DOI | MR | Zbl

[12] Gregory D. A., Pullman N. J., “Prime Boolean matrices, a graph theoretic approach”, Ars Combinatoria, 12 (1981), 81–110 | MR | Zbl

[13] Gregory D. A., Pullman N. J., “Semiring rank: Boolean rank and nonnegative rank factorization”, J. Combin. Inform. Syst. Sci., 8:3 (1983), 223–233 | MR | Zbl

[14] Kim K. H., Boolean Matrix Theory and Applications, Marcel Dekker, New York, 1982 | MR | Zbl

[15] Richman D. J., Schneider H., “Primes in the semigroup of nonnegative matrices”, Linear and Multilinear Algebra, 2 (1974), 135–140 | DOI | MR | Zbl

[16] Tchuente M., On the Decomposition of Boolean Matrices, Univ. of Grenoble, Grenoble, 1980