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Algebra universalis

, 80:18 | Cite as

On the primeness of locally finite idempotent 3-permutability

  • Alberto ChiccoEmail author
Article
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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.

Keywords

Congruence 3-permutable variety Idempotent Locally finite Maltsev condition Prime Special Hagemann relation 

Mathematics Subject Classification

08B05 08A30 03C05 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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