Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-16T12:45:11.582Z Has data issue: false hasContentIssue false
  • English
  • Français

α-Representable coproducts of distributive lattices

Published online by Cambridge University Press:  20 January 2009

Fawzi M. Yaqub
Fawzi M. Yaqub
Affiliation:
Mathematics Department, American University of Beirut, Lebanon
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.

There are a number of classes of distributive lattices whose members can be characterised as the coproduct A * L of suitable distributive lattices A and L. For example, Post algebras [1], pseudo-Post algebras [4], Post Lalgebras ([6], [8[9]) and the lattices [D]n of [4]. Moreover, the α-completeness and α-representability of some(though not all) of these algebras have been investigated in [7], [2], [6], and [10].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 3 , October 1982 , pp. 229 - 235
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Balbes, R. and Dwinger, Ph., Distributive Lattices (University of Missouri Press, Columbia, (1974)Google Scholar
2.Dwinger, Ph., Notes on Post algebras I and II, Indag. Math. 28 (1966), 462–478.CrossRefGoogle Scholar
3.Dwinger, Ph., Introduction to Boolean algebras (Physica. Verlag, Wurzburg, second edition, 1971).Google Scholar
4.Rousseau, G., Post algebras and pseudo-Post algebras, Fund. Math. 67 (1970), 133–145.CrossRefGoogle Scholar
5.Sikorski, R., Products of abstract algebras, Fund. Math. 39 (1952), 211–228.CrossRefGoogle Scholar
6.Speed, T. P., A note on Post algebras, Coll. Math. 24 (1971), 37–44.CrossRefGoogle Scholar
7.Traczyk, T., A generalization of the Loomis-Sikorski theorem, Colloq. Math. 12 (1964), 156–161.CrossRefGoogle Scholar
8.Yaqub, F. M., Free Post L-algebras, Algebra Universalis 9 (1979), 45–53.CrossRefGoogle Scholar
9.Yaqub, F. M., Equationally definable Post L-algebras, Algebra Universalis (to appear).Google Scholar
10.Yaqub, F. M., Representation of Post L-algebras by rings of sets, Proc. Algebra and Geometry Conference, Kuwait University (to appear).Google Scholar