Small representations of finite distributive lattices as congruence lattices
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- by George Grätzer, Ivan Rival and Nejib Zaguia
- Proc. Amer. Math. Soc. 123 (1995), 1959-1961
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301499-7
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Correction: Proc. Amer. Math. Soc. 126 (1998), 2509-2510.
Abstract:
A recent result of G. Grätzer, H. Lakser, and E. T. Schmidt states that for any distributive lattice D with n join-irreducible elements, there exists a lattice L with $O({n^2})$ elements, whose congruence lattice ConL is isomorphic to D. We show that this result is best possible.References
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- George Grätzer, On the congruence lattice of a lattice, The Dilworth theorems, Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1990, pp. 460–464. MR 1111511
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1959-1961
- MSC: Primary 06B10; Secondary 06D05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301499-7
- MathSciNet review: 1301499