A property of transferable lattices
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- by G. Grätzer PDF
- Proc. Amer. Math. Soc. 43 (1974), 269-271 Request permission
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.References
- Kirby A. Baker and Alfred W. Hales, From a lattice to its ideal lattice, Algebra Universalis 4 (1974), 250–258. MR 364036, DOI 10.1007/BF02485732
- H. S. Gaskill, On transferable semilattices, Algebra Universalis 2 (1972), 303–316. MR 323653, DOI 10.1007/BF02945041
- H. S. Gaskill, On transferable semilattices, Algebra Universalis 2 (1972), 303–316. MR 323653, DOI 10.1007/BF02945041 H. Gaskill and C. R. Platt, Transferable lattices (manuscript).
- George Grätzer, Universal algebra, Trends in Lattice Theory (Sympos., U.S. Naval Academy, Annapolis, Md., 1966) Van Nostrand Reinhold, New York, 1970, pp. 173–210. MR 0281674
Additional Information
- © Copyright 1974 American Mathematical Society
- 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