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Proceedings of the American Mathematical Society

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A property of transferable lattices


Author: G. Grätzer
Journal: Proc. Amer. Math. Soc. 43 (1974), 269-271
MSC: Primary 06A20
DOI: https://doi.org/10.1090/S0002-9939-1974-0335378-5
MathSciNet review: 0335378
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Abstract: A lattice $ K$ is transferable if whenever $ K$ can be embedded into the ideal lattice of a lattice $ L$, then $ K$ can be embedded in $ L$. An element is called doubly reducible if it is both join- and meet-reducible. In this note it is proved that every lattice can be embedded into the ideal lattice of a lattice with no doubly reducible element. It follows from this result that a transferable lattice has no doubly reducible element.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0335378-5
Keywords: Lattice, transferable, doubly reducible, ideal lattice
Article copyright: © Copyright 1974 American Mathematical Society

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