1996/04/01 by Keith A. Kearnes, Kearnes, Keith A., Ágnes Szendrei +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/9604246
openalex publication_date 1996/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.