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A Note on Stone Lattices

Published online by Cambridge University Press:  20 November 2018

T. P. Speed
T. P. Speed*
Affiliation:
The University, Sheffield, U.K.
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Stone lattices can be considered as forming a category of abstract algebras and thus there is a forgetful functor from this category to the category of distributive lattices with zero and unit. In this note we consider Stone lattices in this light (cf. [3], [4]) and describe an adjoint to the forgetful functor. The Stone extension of a distributive lattice with zero unit which we obtain differs markedly from the one given in [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 81 - 86
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Chen, C. C., Free stone extensions of distributive lattices, Nanta Mathematica, 2 (1968), 1-15.Google Scholar
2. Chen, C. C. and Grätzer, G., Stone lattices I, II, Canad. J. Math., 21 (1969), 884-903.Google Scholar
3. Grätzer, G., A generalization of Stone's representation theorem for Boolean algebras, Duke Math. J. 30 (1963), 469-474.Google Scholar
4. Grätzer, G.,Stone algebras form an equational class, J. Austral. Math. Soc, 9 (1969), 308-309.Google Scholar
5. Kist, J., Minimal prime ideals in commutative semigroups, Proc. Lond. Math. Soc. Ser. 3, 13 (1963), 31-50.Google Scholar
6. Speed, T. P., On Stone lattices, J. Austral. Math. Soc. 9 (1969), 297-307 Google Scholar