The relationship between two commutators

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We clarify the relationship between the linear commutator and the ordinary commutator by showing that in any variety satisfying a nontrivial idempotent Mal'cev condition the linear commutator is definable in terms of the centralizer relation. We derive from this that abelian algebras are quasi-affine in such varieties. We refine this by showing that if A is an abelian algebra and V(A) satifies an idempotent Mal'cev condition which fails to hold in the variety of semilattices, then A is affine.

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Rings and Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/153038

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9604246
 http://arxiv.org/abs/math/9604246

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arXiv