Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T00:58:18.375Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Triple Characterization for Stone Algebras

Published online by Cambridge University Press:  20 November 2018

Raymond Balbes
Raymond Balbes*
Affiliation:
University of Missouri-St. Louis, St. Louis, Missouri
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 [1], C. C. Chen and G. Grâtzer developed a method for studying Stone algebras by associating with each Stone algebra L, a uniquely determined triple (C(L), D(L), ɸ (L)), consisting of a Boolean algebra C(L), a distributive lattice D(L), and a connecting map ɸ(L). This approach has been successfully exploited by various investigators to determine properties of Stone algebras (e.g. H. Lakser [9] characterized the injective hulls of Stone algebras by means of this technique). The present paper is a continuation of this program.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 852 - 859
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Chen, C. C. and Grâtzer, G., Stone lattices: Construction theorems, Can. J. Math. 21 (1969), 884–894.Google Scholar
2. Stone lattices: Structure theorems, Can. J. Math. 21 (1969), 895–903.Google Scholar
3. Grâtzer, G., Lattice theory: First concepts and distributive lattices (W. H. Freeman Co., San Francisco, 1971).Google Scholar
4. Grâtzer, G. and Lakser, H., The structure of pseudocomplemented distributive lattices, II: Congruence extension and amalgamation, Trans. Amer. Math. Soc. 156 (1971), 343–348.Google Scholar
5. Grâtzer, G. and Lakser, H., The structure of pseudo complemented distributive lattices, III: Infective and absolute subretracts, Trans. Amer. Math. Soc. 157 (1972), 475–487.Google Scholar
6. Jonsson, B., A Boolean algebra without proper automorphisms, Proc. Amer. Math. Soc. 2 (1951), 766–770.Google Scholar
7. Katrinâk, T., A new proof of the construction theorem for Stone algebras, Proc. Amer. Math. Soc. 40 (1973), 75–79.Google Scholar
8. Lakser, H., The structure of pseudocomplemented distributive lattices; I: Subdirect decomposition, Trans. Amer. Math. Soc. 156 (1971), 335–342.Google Scholar
9. Lakser, H., Infective hulls of Stone algebras, Proc. Amer. Math. Soc. 24 (1970), 524–529.Google Scholar
10. Nachbin, L., Une Propriété caractéristique des algebras Booléinnes, Portugal. Math. 6 (1947), 115–118.Google Scholar
11. Stone, M. H., Topological representations of distributive lattices and Brouwerian logics, Casopis Pest. Mat. 67 (1937), 1–25.Google Scholar
12. Varlet, J., On the characterization of Stone lattices, Acta Sci. Math. (Szeged) 27 (1966), 81–84.Google Scholar