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High Quality Content by WIKIPEDIA articles! In abstract algebra, a commutant-associative algebra is a nonassociative algebra over a field whose multiplication satisfies the following axiom: ([A1,A2],[A3,A4],[A5,A6]) = 0, where [A, B] = AB BA is the commutator of A and B and (A, B, C) = (AB)C A(BC) is the associator of A, B and C. In other words, an algebra M is commutant-associative if the commutant, i.e. the subalgebra of M generated by all commutators [A, B], is an associative algebra.