Abstract

LetAbe a prime ring with involution ∗, letSbe the symmetric elements, letKbe the skew elements, letQmlbe the maximal left ring of quotients,x1,…,xmnoncommuting variables, andEi,Fj,Gk,Hl:Am−1→Qml,i,j,k,l=1,2,…,m. We study functional identities of the form ∑mi=1Eiixi+∑mj=1xjFjj+∑mk=1Gkkx*k+∑ml=1x*lHll=0 for allx1,…,xm∈A(whereEiimeansEi(x1,…,x̂i,…,xm), etc.). In caseS∪Kis not algebraic of bounded degree ≤2mdefinitive results are obtained. As an applicationk-commuting traces of symmetricn-additive maps of eitherSorKintoQmlare characterized.

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