A normal form theorem for lattices completely generated by a subset
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- by George Grätzer and David Kelly PDF
- Proc. Amer. Math. Soc. 67 (1977), 215-218 Request permission
Abstract:
For an $\mathfrak {m}$-complete lattice L ($\mathfrak {m}$ is an infinite regular cardinal) and subset X of L that $\mathfrak {m}$-generates L, we prove a Normal Form Theorem for elements of L expressed as polynomials over X. This generalizes a theorem of B. Jónsson in which such a representation is found for the lattice L freely $\mathfrak {m}$-generated by a poset X. We also apply this result to free $\mathfrak {m}$-products of $\mathfrak {m}$-complete lattices.References
- Peter Crawley and Richard A. Dean, Free lattices with infinite operations, Trans. Amer. Math. Soc. 92 (1959), 35–47. MR 108447, DOI 10.1090/S0002-9947-1959-0108447-9 G. Grätzer and D. Kelly, Free $\mathfrak {m}$-products of lattices (to appear). See also Notices Amer. Math. Soc. 24 (1977), A-1, A-221, A-287.
- Bjarni Jónsson, Arithmetic properties of freely $\alpha$-generated lattices, Canadian J. Math. 14 (1962), 476–481. MR 137668, DOI 10.4153/CJM-1962-038-3
- H. Lakser, Normal and canonical representations in free products of lattices, Canadian J. Math. 22 (1970), 394–402. MR 265232, DOI 10.4153/CJM-1970-048-3
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 215-218
- MSC: Primary 06A23
- DOI: https://doi.org/10.1090/S0002-9939-1977-0463058-7
- MathSciNet review: 0463058