The amalgamation property for varieties of lattices

The amalgamation property for varieties of lattices
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Trans. Amer. Math. Soc. 286 (1984), 251-256

DOI: https://doi.org/10.1090/S0002-9947-1984-0756038-3

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There are precisely three varieties of lattices that satisfy the amalgamation property: trivial lattices, distributive lattices, and all lattices.

References

Alan Day, Splitting lattices generate all lattices, Algebra Universalis 7 (1977), no. 2, 163–169. MR 434897, DOI 10.1007/BF02485425
Alan Day, Characterizations of finite lattices that are bounded-homomorphic images of sublattices of free lattices, Canadian J. Math. 31 (1979), no. 1, 69–78. MR 518707, DOI 10.4153/CJM-1979-008-x
G. Grätzer, B. Jónsson, and H. Lakser, The amalgamation property in equational classes of modular lattices, Pacific J. Math. 45 (1973), 507–524. MR 366768
Jaroslav Ježek and Václav Slavík, Primitive lattices, Czechoslovak Math. J. 29(104) (1979), no. 4, 595–634 (English, with Russian summary). MR 548223
Bjarni Jónsson, Universal relational systems, Math. Scand. 4 (1956), 193–208. MR 96608, DOI 10.7146/math.scand.a-10468
Ralph McKenzie, Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc. 174 (1972), 1–43. MR 313141, DOI 10.1090/S0002-9947-1972-0313141-1
Richard S. Pierce, Introduction to the theory of abstract algebras, Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1968. MR 0227070

A note on the amalgamation property in lattice varieties