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Single identities for lattice theory and for weakly associative lattices

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Abstract

We present a single identity for the variety of all lattices that is much simpler than those previously known to us. We also show that the variety of weakly associative lattices is one-based, and we present a generalized one-based theorem for subvarieties of weakly associative lattices that can be defined with absorption laws. The automated theorem-proving program Otter was used in a substantial way to obtain the results.

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Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, 60439-4844, Argonne, IL, USA

    W. McCune

  2. Department of Mathematics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    R. Padmanabhan

Authors
  1. W. McCune
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  2. R. Padmanabhan
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Additional information

Supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38.

Supported by an operating grant from NSERC of Canada (#A8215).

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McCune, W., Padmanabhan, R. Single identities for lattice theory and for weakly associative lattices. Algebra Universalis 36, 436–449 (1996). https://doi.org/10.1007/BF01233914

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  • DOI: https://doi.org/10.1007/BF01233914

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