Representable tolerances in varieties

zbMATH Open1299.08003arXiv1205.3471MaRDI QIDQ5402854

Paolo Lipparini

Publication date: 17 March 2014

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 $imes$ L. This is related to recent results by G. Cz'edli and E. W. Kiss.

Full work available at URL: https://arxiv.org/abs/1205.3471

zbMATH Keywords

latticetolerancevarietyquasivarietyrepresentable3-permutable varietyimage of a congruence

Mathematics Subject Classification ID

Partial orders, general (06A06) Structure theory of lattices (06B05) Lattice ideals, congruence relations (06B10) Subalgebras, congruence relations (08A30) Quasivarieties (08C15) Varieties of lattices (06B20) Generalizations of lattices (06B75)

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