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On the primeness of locally finite idempotent 3-permutability

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Abstract

In this paper, we show that for any finite idempotent non-congruence 3-permutable algebra \(\mathbf {A}\), it is always the case that \({{\,\mathrm{HSP}\,}}(\mathbf {A})\) contains an algebra carrying a binary reflexive compatible relation having a certain shape, which we have called a 2-dimensional special Hagemann relation with middle part. As a result of this property, we are able to show that the join of any pair of locally finite idempotent non-congruence 3-permutable varieties in the lattice of interpretability types, fails to be congruence 3-permutable, yielding a primeness argument for this specific setting.

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  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Alberto Chicco

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  1. Alberto Chicco
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Correspondence to Alberto Chicco.

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Chicco, A. On the primeness of locally finite idempotent 3-permutability. Algebra Univers. 80, 18 (2019). https://doi.org/10.1007/s00012-019-0594-4

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  • DOI: https://doi.org/10.1007/s00012-019-0594-4

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