When is the free product of lattices complete?
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- by George Grätzer and David Kelly
- Proc. Amer. Math. Soc. 66 (1977), 6-8
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460199-5
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Abstract:
Yu. I. Sorkin proved that, up to isomorphism, there are three finite lattices that can be represented as a free product of two lattices. In this note we prove that, up to isomorphism, there are five complete lattices that can be so represented.References
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- Bjarni Jónsson, Sublattices of a free lattice, Canadian J. Math. 13 (1961), 256–264. MR 123493, DOI 10.4153/CJM-1961-021-0
- Howard L. Rolf, The free lattice generated by a set of chains, Pacific J. Math. 8 (1958), 585–595. MR 103843, DOI 10.2140/pjm.1958.8.585
- Yu. I. Sorkin, Free unions of lattices, Mat. Sbornik N.S. 30(72) (1952), 677–694 (Russian). MR 0047605
- Philip M. Whitman, Free lattices, Ann. of Math. (2) 42 (1941), 325–330. MR 3614, DOI 10.2307/1969001
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 6-8
- MSC: Primary 06A23
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460199-5
- MathSciNet review: 0460199