Abstract
It is shown that if
is any variety of algebras all of whose congruence lattices are modular, then the congruence lattice of every algebra in
satisfies the Arguesian law.
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References
Ralph Freese,Congruence modularity, Preliminary Report, Notices Amer. Math. Soc.22 (1975), p. A-301.
G. Grätzer, B. Jónsson andH. Lakser,The amalgamation property in classes of modular lattices, Pacific J. of Math.45 (1973), 507–524.
B. Jónsson,The class of Arguesian lattices is selfdual, Algebra Universalis2 (1973), p. 396.
J. B. Nation,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis4 (1974), 78–88.
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This work was supported in part by NSF grants Nos. 73-08589 A02 and GP-29129 A-3.
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Freese, R., Jónsson, B. Congruence modularity implies the Arguesian identity. Algebra Universalis 6, 225–228 (1976). https://doi.org/10.1007/BF02485830
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DOI: https://doi.org/10.1007/BF02485830