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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite transferable lattices are sharply transferable
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by C. R. Platt PDF
Proc. Amer. Math. Soc. 81 (1981), 355-358 Request permission

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
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 355-358
  • MSC: Primary 06B05
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0597639-8
  • MathSciNet review: 597639