Residuation theory and Boolean matrices
Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 185-190
Voir la notice de l'article provenant de la source Cambridge University Press
We begin this paper by considering a Boolean algebra as a lattice which is relatively pseudo-complemented (i.e., residuated with respect to intersection) and give, in this case, certain properties of the equivalences of types A, B and F(as introduced by Molinaro [1]). We then show how these results carry over to the case of Boolean matrices, which form a Boolean algebra residuated also with respect to matrix multiplication. Other properties of matrix residuals are established and we conclude with three algebraic characterisations of invertible Boolean matrices.
Blyth, T. S. Residuation theory and Boolean matrices. Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 185-190. doi: 10.1017/S2040618500034997
@article{10_1017_S2040618500034997,
author = {Blyth, T. S.},
title = {Residuation theory and {Boolean} matrices},
journal = {Glasgow mathematical journal},
pages = {185--190},
year = {1964},
volume = {6},
number = {4},
doi = {10.1017/S2040618500034997},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034997/}
}
[1] 1.Molinaro, I., Demi-groupes résidutifs, D. ès Sc. thesis, Paris, 1956; also J. Math. Pures Appl. 39 (1960), 319–356 and 40 (1961), 43–110. Google Scholar
[2] 2.Luce, R. D., A note on Boolean matrix theory, Proc. Amer. Math. Soc. 3 (1952), 382–388. Google Scholar | DOI
[3] 3.Rutherford, D. E., Inverses of Boolean matrices, Proc. Glasgow Math. Assoc. 6 (1963), 49–53. Google Scholar | DOI
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