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 is called *transferable* if and only if, whenever can be embedded into the lattice of all ideals of a lattice , can be embedded into itself. If for every lattice embedding of into there exists an embedding of into satisfying the further condition that for and in , holds if and only if , then is called *sharply transferable*. It is shown that every finite transferable lattice is sharply transferable.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0597639-8

Keywords:
Lattice,
transferable,
ideal lattice

Article copyright:
© Copyright 1981
American Mathematical Society