Commuting traces of multiadditive mappings

[摘要] Let R be a prime ring and M an n-additive mapping on R such that [M(x,..., x), x] = 0 for all x is an element of R. If char R = 0 or > n, then there exist mappings mu(i) of R into the extended centroid C of R such that M(x,...,x) = Sigma(i=0)(n)mu(i)(x)x(n-i) for all x is an element of R. If, in addition, R is not algebraic of bounded degree less than or equal to n, then for each i there exists an i-additive mapping M-i of R-i into C such that mu(i)(x) = M-i(x,..., x) for all x is an element of R. (C) 1997 Academic Press.

[发布日期] 1997-07-15