Some applications of higher commutators in Mal’cev algebras

@article{Aichinger2010SomeAO,
  title={Some applications of higher commutators in Mal’cev algebras},
  author={E. Aichinger and Nebojsa Mudrinski},
  journal={Algebra universalis},
  year={2010},
  volume={63},
  pages={367-403}
}
We establish several properties of Bulatov’s higher commutator operations in congruence permutable varieties. We use higher commutators to prove that for a finite nilpotent algebra of finite type that is a product of algebras of prime power order and generates a congruence modular variety, affine completeness is a decidable property. Moreover, we show that in such algebras, we can check in polynomial time whether two given polynomial terms induce the same function. 
41 Citations
On supernilpotent algebras
Mal’cev algebras with supernilpotent centralizers
Bounding the free spectrum of nilpotent algebras of prime power order
The equation solvability problem over nilpotent Mal'cev algebras
Higher Kiss Terms
2-Supernilpotent Mal’cev algebras
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