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Finite forbidden lattices

Part of the Lecture Notes in Mathematics book series (LNM,volume 1004)

Abstract

Let L be any finite simple lattice of at least three elements, whose co-atoms intersect to 0. One principal result of the paper is that L is not dual isomorphic to the lattice of subvarieties of any locally finite variety. A second principal result is that these statements are equivalent: (i) L is isomorphic to the congruence lattice of a finite algebra with one basic operation; (ii) L is isomorphic either to the subspace lattice of a finite vector space, or for some permutation σ of a finite domain, to the lattice of equivalence relations invariant under σ.

Keywords

  • Binary Operation
  • Basic Operation
  • Unary Operation
  • Unary Algebra
  • Congruence Lattice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported by National Science Foundation grant MCS-8103455.

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© 1983 Springer-Verlag

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McKenzie, R. (1983). Finite forbidden lattices. In: Freese, R.S., Garcia, O.C. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063438

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  • DOI: https://doi.org/10.1007/BFb0063438

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12329-3

  • Online ISBN: 978-3-540-40954-0

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