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 Là â L. This is related to recent results by G. Czà ©dli, G. Grà ¤tzer and E. W. Kiss.
Lipparini, P. (2013). Representable tolerances in varieties. ACTA SCIENTIARUM MATHEMATICARUM, 79(1-2), 3-16.
Representable tolerances in varieties
LIPPARINI, PAOLO
2013-01-01
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 Là â L. This is related to recent results by G. Czà ©dli, G. Grà ¤tzer and E. W. Kiss.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
