Matrices over orthomodular lattices
Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 55-59
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper elementary properties are established for matrices whose coordinates are elements of a lattice L. In particular, many of the results of Luce [4] are extended to the case where L is an orthomodular lattice, a lattice with an orthocomplementation denoted by in which a ≦ b ⇒ a ∨(a′ ∧ b) = b. Originally, these were called orthocomplemented weakly modular lattices, Foulis [2]. In Theorem 1 a characterization is given of the nucleus with respect to matrix multiplication, which is in general nonassociative. Matrices with A-1 = transpose (A) are characterized in Lemma 8. Theorems 3 and 4 respectively, give partial characterizations of zero divisors and inverses.
Bevis, J. H. Matrices over orthomodular lattices. Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 55-59. doi: 10.1017/S0017089500000537
@article{10_1017_S0017089500000537,
author = {Bevis, J. H.},
title = {Matrices over orthomodular lattices},
journal = {Glasgow mathematical journal},
pages = {55--59},
year = {1969},
volume = {10},
number = {1},
doi = {10.1017/S0017089500000537},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000537/}
}
[1] 1.Blyth, T. S., ∧-distributive Boolean matrices, Proc. Glasgow Math. Assoc. 7 (1965), 93–100. Google Scholar | DOI
[2] 2.Foulis, D. J., Baer *-semigroups, Proc. Amer. Math. Soc. 11 (1960), 648–654. Google Scholar
[3] 3.Foulis, D. J., A note on orthomodular lattices, Portugal. Math. 21 (1962), 65–72. Google Scholar
[4] 4.Luce, R. D., A note on Boolean matrix theory, Proc. Amer. Math. Soc. 3 (1952), 382–388. Google Scholar | DOI
[5] 5.Rutherford, D. E., Inverses of Boolean matrices, Proc. Glasgow Math. Assoc. 6 (1963), 49–53. Google Scholar | DOI
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