Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-27T02:10:49.539Z Has data issue: false hasContentIssue false
  • English
  • Français

On functions and equations in distributive lattices

Published online by Cambridge University Press:  20 January 2009

Sergiu Rudeanu
Sergiu Rudeanu
Affiliation:
Institute of Mathematics, Eminescu Str. 47, Bucharest 9, Rumania
Rights & Permissions [Opens in a new window]

Summary

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], R. L. Goodstein has extended some well-known theorems on functions and equations in a Boolean algebra to the case of a distributive lattice L with 0 and 1. The purpose of this paper is to prove that most of Goodstein's theorems, as well as some additional results, are still valid in the case when L is not required to have least and greatest elements.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 1 , June 1968 , pp. 49 - 54
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

REFERENCES

(1) Goodstein, R. L., The Solution of Equations in a Lattice, Proc. Roy. Soc. Edinburgh, Sect. A, 67 (1966/1967), 231–242.Google Scholar
(2) Gotō, M., On the General Solution of a Logical Algebraic Equation with Many Unknowns (in Japanese), Bull. Electr. Lab. 20 (1956), 81–87.Google Scholar
(3) Grebenščikov, V. N., Coalitions of Systems of Equations of a Boolean Algebra and their Solution (in Russian), Dokl. Akad. Nauk SSSR, 141 (1961), 1317–1319.Google Scholar
(4) LÖwenheim, L., Uber die Auflösung von Gleichungen im logischen Gebietkalkul. Math. Ann. 68 (1910), 169–207.CrossRefGoogle Scholar
(5) Rudeanu, S., Boolean Equations and their Applications to the Study of Bridge Circuits. II. (in Romanian). Com. Acad. R.P. Romîne 12 (1961), 611–618.Google Scholar
(6) Rudeanu, S., Remarks on Motinori Gotō's Papers on Boolean Equations, Rev. Roumaine Math. Pures Appl. 10 (1965), 311–317.Google Scholar
(7) Whitehead, A. N., A Treatise on Universal Algebra, With Applications (Cambridge, 1898).Google Scholar