Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-12T21:19:56.888Z Has data issue: false hasContentIssue false
  • English
  • Français

Functions and equations in classes of distributive lattices with pseudocomplementation

Published online by Cambridge University Press:  20 January 2009

R. Beazer
R. Beazer
Affiliation:
The University of Glasgow, Glasgow G12 8QW
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 (8), R. L. Goodstein gave necessary and sufficient conditions for the solvability of equations over distributive lattices with 0 and 1 together with an algorithm for computing a solution whenever one exists. In addition, the same problem was considered for a special class of equations over distributive lattices with pseudocomplementation. The validity of several of Goodstein's results for distributive lattices without 0 and 1 was pointed out by Rudeanu in (15) and (16).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 2 , September 1974 , pp. 191 - 203
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Balbes, R. and Dwinger, PH., Coproducts of Boolean algebras and chains with applications to Post algebras, Colloq. Math. 24 (1971), 15–25.CrossRefGoogle Scholar
(2) Balbes, R. and Dwinger, PH., Uniqueness of representations of a distributive lattice as a free product of a Boolean algebra and a chain, Colloq. Math. 24 (1971), 27–35.CrossRefGoogle Scholar
(3) Balbes, R., On free pseudo-complemented and relatively pseudo-complemented semi-lattices, Fund. Math. 78 (1973), 119–131.CrossRefGoogle Scholar
(4) Beazer, R., Some remarks on Post algebras, Colloq. Math. 29 (1974), 167–178.CrossRefGoogle Scholar
(5) Beazer, R., Intrinsic topologies on Brouwerian semilattices, Proc. London Math. Soc. 28 (1974), 311–334.CrossRefGoogle Scholar
(6) Beazer, R., Hierarchies of distributive lattices satisfying annihilator conditions, J. London Math. Soc. (to appear).Google Scholar
(7) Epstein, G., The lattice theory of Post algebras, Trans. Amer. Math. Soc. 95 (1960), 300–317.CrossRefGoogle Scholar
(8) Goodstein, R. L., The solution of equations in a lattice, Proc. Roy. Soc. Edinburgh Section A 67 (1966/1967), 231–242.Google Scholar
(9) GrÄtzer, G., On Boolean functions (Notes on lattice theory III), Rev. Roumaine Math. Pures Appl. 7 (1962), 693–697.Google Scholar
(10) GrÄtzer, G., Boolean functions on distributive lattices, Acta. Math. Acad. Sci. Hungar. 15 (1964), 195–201.CrossRefGoogle Scholar
(11) GrÄTzer, G., Lattice Theory (Freeman, San Francisco, 1971).Google Scholar
(12) Iskander, A., Algebraic functions onp-rings, Colloq. Math. 25 (1972), 37–41.CrossRefGoogle Scholar
(13) Mckinsey, J. C. C. and Tarski, A., On closed elements in closure algebras, Ann. of Math. 47 (1946), 122–162.CrossRefGoogle Scholar
(14) Rouseau, G., Post algebras and pseudo-Post algebras, Fund. Math. 67 (1970), 133–145.CrossRefGoogle Scholar
(15) Rudeanu, S., On functions and equations in distributive lattices, Proc. Edinburgh Math. Soc. 16 (1968), 49–54.CrossRefGoogle Scholar
(16) Rudeanu, S., Correction to the paper “On functions and equations in distri-butive lattices”, Proc. Edinburgh Math. Soc. 17 (1970), 105.CrossRefGoogle Scholar