Some applications of higher commutators in Mal'cev algebras
Many properties of higher commutators in congruence-permutable varieties are derived. Let \(A\) be a finite nilpotent algebra of finite type that is a product of algebras of prime power order and generates a congruence-modular variety. Using higher commutators, the following results are proved: There is an algorithm that decides whether every congruence-preserving function on \(A\) is a polynomial function on \(A\) or not. The problem of deciding if two given polynomial terms of \(A\) induce the same function has polynomial time complexity in the length of the input terms.
scientific article; zbMATH DE number 5818038
scientific article