Reflexive Relations and Mal’tsev Conditions for Congruence Lattice Identities in Modular Varieties
نویسندگان
چکیده
Based on a property of tolerance relations, it was proved in [3] 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 [3] is not the simplest known one in general. Now we extend the result of [3] from tolerances to reflexive compatible relations. This leads to a construction of simpler Mal’tsev conditions for lattice identities implying modularity. Notice that Day terms and Jónsson terms, as Mal’tsev conditions, are just particular cases of the general construction.
منابع مشابه
All congruence lattice identities implying modularity have
For an arbitrary lattice identity implying modularity (or at least congruence modularity) a Mal’tsev condition is given 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. This research was partially supported by the NFSR of Hungary (OTKA), grant no. T034137 and T026243, and also by the Hungarian...
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