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Elementary equivalence and relatively free products of lattices

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Abstract

It is shown that if

is a non-trivial variety of lattices, then there existA, B, C ∈

such thatB≡C but notA*B≡A*C. Except in the case when

is the variety of all distributive lattices,A can be taken to consist of just one element. For the varietyD of all distributive lattices, it is shown that for anyB, C and any finiteA, B≡C if and only ifA*B≡A*C.

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Authors and Affiliations

  1. Vanderbilt University, Nashville, Tennessee, USA

    Bjarni Jónsson & Philip Olin

  2. York University, Downsview, Ontario, Canada

    Bjarni Jónsson & Philip Olin

Authors
  1. Bjarni Jónsson
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  2. Philip Olin
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Additional information

The work of the first author was supported in part by NSF Grant GP-29129, and the work of the second author by a grant from the N.R.C. of Canada.

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Jónsson, B., Olin, P. Elementary equivalence and relatively free products of lattices. Algebra Universalis 6, 313–325 (1976). https://doi.org/10.1007/BF02485839

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  • DOI: https://doi.org/10.1007/BF02485839

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