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Proceedings of the American Mathematical Society

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

 

 

A normal form theorem for lattices completely generated by a subset


Authors: George Grätzer and David Kelly
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0463058-7
Keywords: Complete lattice, representation, join-irreducible
Article copyright: © Copyright 1977 American Mathematical Society