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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite transferable lattices are sharply transferable


Author: C. R. Platt
Journal: Proc. Amer. Math. Soc. 81 (1981), 355-358
MSC: Primary 06B05
MathSciNet review: 597639
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Abstract: A lattice $ \mathfrak{L}$ is called transferable if and only if, whenever $ \mathfrak{L}$ can be embedded into the lattice $ I(\mathcal{K})$ of all ideals of a lattice $ \mathcal{K}$, $ \mathfrak{L}$ can be embedded into $ \mathcal{K}$ itself. If for every lattice embedding $ f$ of $ \mathfrak{L}$ into $ I(\mathcal{K})$ there exists an embedding $ g$ of $ \mathfrak{L}$ into $ \mathcal{K}$ satisfying the further condition that for $ x$ and $ y$ in $ L$, $ f(x) \in g(y)$ holds if and only if $ x \leqslant y$, then $ \mathfrak{L}$ is called sharply transferable. It is shown that every finite transferable lattice is sharply transferable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0597639-8
PII: S 0002-9939(1981)0597639-8
Keywords: Lattice, transferable, ideal lattice
Article copyright: © Copyright 1981 American Mathematical Society