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Proceedings of the American Mathematical Society

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

 

 

A representation theorem for semilattices


Author: D. A. Bredikhin
Journal: Proc. Amer. Math. Soc. 90 (1984), 219-220
MSC: Primary 06A12; Secondary 06B15
DOI: https://doi.org/10.1090/S0002-9939-1984-0727237-7
MathSciNet review: 727237
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Abstract: We prove that every semilattice $ (L, \wedge )$ admits an embedding $ Q$ into the set $ R(X)$ of all partial orders on some set $ X$ such that for all $ a$, $ b \in L$, $ Q(a \wedge b) = Q(a) \cap Q(b)$ and if $ a \vee b$ exists then also $ Q(a \vee b) = Q(b) \circ Q(a)$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0727237-7
Keywords: Semilattice, representation
Article copyright: © Copyright 1984 American Mathematical Society