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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On generating free products of lattices


Authors: G. Grätzer and J. Sichler
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0344167-7
Keywords: Lattice, free product, generating set
Article copyright: © Copyright 1974 American Mathematical Society