منابع مشابه
An Easy Test for Congruence Modularity
We describe an easy way to determine whether the realization of a set of idempotent identities guarantees congruence modularity or the satisfaction of a nontrivial congruence identity. Our results yield slight strengthenings of Day’s Theorem and Gumm’s Theorem, which each characterize congruence modularity.
متن کاملCongruence lower semimodularity and 2-finiteness imply congruence modularity
We show that any congruence lower semimodular variety whose 2-generatecl free algebra is finite must be congruence modular.
متن کامل3 - 3 lattice inclusions imply congruence modularity
The complexity of a lattice polynomial is defined inductively, with variables having complexity 0. If p=plv'"vOk or p=plA'''/XOk is the canonical expression of the polynomial O, then the complexity c(p) = l+max{c(p~):l<-i-k}. An n-k lattice inclusion is an inclusion of the form p <-o-with c(p)<-n and c(o-)-k. In this note we use the main result of Day [1] to show that if all the congruence latt...
متن کاملAll 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...
متن کاملCongruence Modularity Implies Cyclic Terms for Finite Algebras
An n-ary operation f : An → A is called cyclic, if it is idempotent and f(a1, a2, a3, . . . , an) = f(a2, a3, . . . , an, a1) for every a1, . . . , an ∈ A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2012
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-012-0186-z