Abstract
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.
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Presented by R. Freese.
The second author is supported by Grant No. 144011 of the Ministry of Science of the Republic of Serbia, and the Scholarship ‘One-Month Visits to Austria for University Graduates’ WUS-Austria from the Austrian Ministry of Education, Science and Culture.
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Aichinger, E., Mudrinski, N. Some applications of higher commutators in Mal’cev algebras. Algebra Univers. 63, 367–403 (2010). https://doi.org/10.1007/s00012-010-0084-1
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DOI: https://doi.org/10.1007/s00012-010-0084-1