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Some Remarks on a Class of Distributive Lattices

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
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Distributive pseudo-complemented lattices form an extensively studied class of distributive lattices. Examples are the lattice of all open sets of a topological space, the lattice of all ideals of a distributive lattice with zero and the lattice of all congruences of an arbitrary lattice. Lattice which are just pseudo-complemented have been studied in detail by J. Varlet [6], [7] where, however, the most interesting results require at least the assumption of modularity, sometimes distributivity.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 289 - 296
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Birkhoff, G., ‘Lattice Theory’. Amer. Math. Soc. Colloq. (1948).Google Scholar
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[3]Kist, J., ‘Minimal prime ideals in commutative semigroups’. Proc. Lond. Math. Soc. Ser 3 13 (1963), 31–50.CrossRefGoogle Scholar
[4]Speed, T. P., ‘A note on commutative semigroups’ J. Aust. Math. Soc. 8 (1968), 731–736.CrossRefGoogle Scholar
[5]Speed, T. P., ‘On Stone lattices’ J. Aust. Math. Soc. 9 (1969), 297–307.CrossRefGoogle Scholar
[6]Varlet, J., ‘Contributions à l'étude des treillis pseudo-complémentés et de treillis de Stone’. Mem. Soc. Roy. des Sci. de Liege 5 ser. 8 (1963), 1–71.Google Scholar
[7]Varlet, J., ‘Contributions a l' étude des treillis pseudo-complémentés et de treillis de Stone’. Thesis: Univ. de Liège (1964).Google Scholar