We show that if a single algebra has a difference term, then many definitions of the commutator coincide. In particular, this applies to the usual TC-commutator, to the 2-terms commutator and to all the n-ary (cyclic) generalizations we shall introduce. However, we show that there is an algebra in a locally finite variety which is abelian in the sense of the cyclic commutators but not abelian in the sense of the linear commutator (i.e., not quasi-affine). In particular, these commutators are generally distinct.
Lipparini, P. (1996). Difference terms and commutators [Altro].
Difference terms and commutators
P. Lipparini
1996-05-01
Abstract
We show that if a single algebra has a difference term, then many definitions of the commutator coincide. In particular, this applies to the usual TC-commutator, to the 2-terms commutator and to all the n-ary (cyclic) generalizations we shall introduce. However, we show that there is an algebra in a locally finite variety which is abelian in the sense of the cyclic commutators but not abelian in the sense of the linear commutator (i.e., not quasi-affine). In particular, these commutators are generally distinct.File in questo prodotto:
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