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arXiv · 1205.3471

Representable tolerances in varieties

Paolo Lipparini
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Abstract

We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety under consideration, while the first way is variety-dependent. The relationships between these two kinds of representations are clarified. As an application, we show that any tolerance on some lattice L is the image of some congruence on a subalgebra of L $\times$ L. This is related to recent results by G. Cz\'edli and E. W. Kiss.

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Paolo Lipparini. 2012-05-15. Representable tolerances in varieties. https://arxiv.org/abs/1205.3471

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