Geodesic
The algebraic structure of the semigroup of binary relations on a finite set
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 57-68

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study some questions proposed by B. Schein [8] regarding the semigroup of binary relations Bx for a finite set X: what is the ideal structure of Bx, what are the congruences on Bx, what are the endomorphisms of Bx? For |X| = nit is convenient to regard Bx as the semigroup Bn of n×n (0, l)-matrices under Boolean matrix multiplication. 
Kim, Ki Hang; Roush, Fred William. The algebraic structure of the semigroup of binary relations on a finite set. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 57-68. doi: 10.1017/S0017089500004468
@article{10_1017_S0017089500004468,
     author = {Kim, Ki Hang and Roush, Fred William},
     title = {The algebraic structure of the semigroup of binary relations on a finite set},
     journal = {Glasgow mathematical journal},
     pages = {57--68},
     year = {1981},
     volume = {22},
     number = {1},
     doi = {10.1017/S0017089500004468},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004468/}
}
TY  - JOUR
AU  - Kim, Ki Hang
AU  - Roush, Fred William
TI  - The algebraic structure of the semigroup of binary relations on a finite set
JO  - Glasgow mathematical journal
PY  - 1981
SP  - 57
EP  - 68
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004468/
DO  - 10.1017/S0017089500004468
ID  - 10_1017_S0017089500004468
ER  - 
%0 Journal Article
%A Kim, Ki Hang
%A Roush, Fred William
%T The algebraic structure of the semigroup of binary relations on a finite set
%J Glasgow mathematical journal
%D 1981
%P 57-68
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004468/
%R 10.1017/S0017089500004468
%F 10_1017_S0017089500004468

[1] 1.Birkhoff, G., Lattice theory (Amer. Math. Soc, 1967). Google Scholar

[2] 2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Math. Surveys No. 7, Amer. Math. Soc. (Providence R. I., 1961). Google Scholar

[3] 3.Kim, K. H. (Butler), A Moore-Penrose inverse for Boolean matrices, Proceedings of Second Australian Conference on Combinatorial Mathematics, Lecture Notes in Mathematics 403 (Springer-Verlag, 1974), 18–28. Google Scholar

[4] 4.Kim, K. H. (Butler), Combinatorial properties of binary semigroups, Period. Math. Hungar. 5 (1974), 3–46. Google Scholar

[5] 5.Plemmons, R. J., Generalized inverses of Boolean relation matrices, SIAM J. Appl. Math. 20 (1971), 426–433. Google Scholar | DOI

[6] 6.Rosenblatt, D., On the graphs of finite idempotent Boolean relation matrices, J. Res. Nat. Bur. Standards, Sect. B 61B–4 (1963), 249–256. Google Scholar | DOI

[7] 7.Ryser, H. J., Combinatorial mathematics (Wiley, 1963). Google Scholar | DOI

[8] 8.Schein, B. M., Problems 1–3, Proceedings of Conference on Algebraic Semigroup Theory, Szeged, Hungary, 08 1972, 64. Google Scholar

[9] 9.Schwarz, Š., On the semigroup of binary relations on a finite set, Czechoslovak Math. J. 20–95 (1970), 632–679. Google Scholar | DOI

[10] 10.Schwarz, Š., On semigroups in combinatorics, Proceedings of Conference on Algebraic Semigroup Theory, Szeged, Hungary, 08 1972, 24–31. Google Scholar

[11] 11.Zaretskii, K. A., Regular elements in the semigroup of binary relations (Russian), Uspehi Mat. Nauk. 17 (1962), 105–108. Google Scholar

Cité par Sources :