Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-09T22:34:53.419Z Has data issue: false hasContentIssue false
  • English
  • Français

The algebraic structure of the semigroup of binary relations on a finite set

Published online by Cambridge University Press:  18 May 2009

Ki Hang Kim  and
Fred William Roush
Ki Hang Kim
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36101, U.S.A.
Fred William Roush
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36101, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 57 - 68
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Birkhoff, G., Lattice theory (Amer. Math. Soc, 1967).Google Scholar
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.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.Kim, K. H. (Butler), Combinatorial properties of binary semigroups, Period. Math. Hungar. 5 (1974), 3–46.Google Scholar
5.Plemmons, R. J., Generalized inverses of Boolean relation matrices, SIAM J. Appl. Math. 20 (1971), 426–433.CrossRefGoogle Scholar
6.Rosenblatt, D., On the graphs of finite idempotent Boolean relation matrices, J. Res. Nat. Bur. Standards, Sect. B 61B–4 (1963), 249–256.CrossRefGoogle Scholar
7.Ryser, H. J., Combinatorial mathematics (Wiley, 1963).CrossRefGoogle Scholar
8.Schein, B. M., Problems 1–3, Proceedings of Conference on Algebraic Semigroup Theory, Szeged, Hungary, 08 1972, 64.Google Scholar
9.Schwarz, Š., On the semigroup of binary relations on a finite set, Czechoslovak Math. J. 20–95 (1970), 632–679.CrossRefGoogle Scholar
10.Schwarz, Š., On semigroups in combinatorics, Proceedings of Conference on Algebraic Semigroup Theory, Szeged, Hungary, 08 1972, 24–31.Google Scholar
11.Zaretskii, K. A., Regular elements in the semigroup of binary relations (Russian), Uspehi Mat. Nauk. 17 (1962), 105–108.Google Scholar