Commuting traces of multiadditive maps on invertible and singular matrices

摘要

Let n > m > 1 be natural numbers, and let M_n(K) be the ring of all n×n matrices over a field K. We describe traces of m-additive maps G: M_n(K)~m → M_n(K) such that [G(x, . . ., x), x] = 0 for all invertible (singular) x ∈ M_n(K), where either char K = 0 or char K > m + 1.