For varieties, congruence modularity is equivalent to the tolerance intersection property, TIP in short. Based on TIP, it was proved in  that for an arbitrary lattice identity implying modularity (or at least congruence modularity) there exists a Mal'tsev condition such that the identity holds in congruence lattices of algebras of a variety if and only if the variety satisfies the corresponding Mal'tsev condition. However, the Mal'tsev condition constructed in  is not the simplest known one in general. Now we improve this result by constructing the best Mal'tsev condition and various related conditions. As an application, we give a particularly easy new proof of the result of Freese and Jonsson  stating that modular congruence varieties are Arguesian, and we strengthen this result by replacing "Arguesian" by "higher Arguesian" in the sense of Haiman . We show that lattice terms for congruences of an arbitrary congruence modular variety can be computed in two steps: the first step mimics the use of congruence distributivity, while the second step corresponds to congruence permutability. Particular cases of this result were known; the present approach using TIP is even simpler than the proofs of the previous partial results.
Czedli, L., Horvath, E.K., & Lipparini, P. (2005). Optimal Mal'tsev conditions for congruence modular varieties. ALGEBRA UNIVERSALIS, 53(2005/03/02), 267-279 [10.1007/s00012-005-1893-5].
|Tipologia:||Articolo su rivista|
|Citazione:||Czedli, L., Horvath, E.K., & Lipparini, P. (2005). Optimal Mal'tsev conditions for congruence modular varieties. ALGEBRA UNIVERSALIS, 53(2005/03/02), 267-279 [10.1007/s00012-005-1893-5].|
|IF:||Con Impact Factor ISI|
|Settore Scientifico Disciplinare:||Settore MAT/02 - Algebra|
|Revisione (peer review):||Esperti anonimi|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00012-005-1893-5|
|Stato di pubblicazione:||Pubblicato|
|Data di pubblicazione:||2005|
|Titolo:||Optimal Mal'tsev conditions for congruence modular varieties|
|Autori:||Czedli, L; Horvath, EK; Lipparini, P|
|Appare nelle tipologie:||01 - Articolo su rivista|