On generating free products of lattices
HTML articles powered by AMS MathViewer
- by G. Grätzer and J. Sichler PDF
- Proc. Amer. Math. Soc. 46 (1974), 9-14 Request permission
Abstract:
For a lattice $K$ let $g(K)$ denote the cardinality of the smallest generating set of $K$. Let $L$ be the free product of the lattices $A$ and $B$. It is proved that $g(L) = g(A) + g(B)$. This is proved, in fact, for free products with respect to any given equational class of lattices. Some applications and generalizations are also given.References
- George Grätzer, Lattice theory. First concepts and distributive lattices, W. H. Freeman and Co., San Francisco, Calif., 1971. MR 0321817
- G. Grätzer, H. Lakser, and C. R. Platt, Free products of lattices, Fund. Math. 69 (1970), 233–240. MR 274351, DOI 10.4064/fm-69-3-233-240
- G. Grätzer and J. Sichler, Free decompositions of a lattice, Canadian J. Math. 27 (1975), 276–285. MR 369195, DOI 10.4153/CJM-1975-034-5
- B. Jónsson, Relatively free products of lattices, Algebra Universalis 1 (1971/72), 362–373. MR 300946, DOI 10.1007/BF02944995
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 9-14
- MSC: Primary 06A20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0344167-7
- MathSciNet review: 0344167