DECOMPOSITIONS OF QUOTIENT RINGS AND m-POWER COMMUTING MAPS

Abstract

Let R be a semiprime ring with symmetric Martindale quotient ring Q, n2 and let f(X)=X(n)h(X), where h(X) is a polynomial over the ring of integers with h(0)= +/- 1. Then there is a ring decomposition Q=Q(1) circle plus Q(2) circle plus Q(3) such that Q(1) is a ring satisfying S2n-2, the standard identity of degree 2n-2, Q(2)M(n)(E) for some commutative regular self-injective ring E such that, for some fixed q>1, x(q)=x for all xE, and Q(3) is a both faithful S2n-2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring.