On Functional Identities in Prime Rings with Involution

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 = 1 Eiixi + ∑mj = 1 xjFjj + ∑mk = 1 Gkkx*k + ∑ml = 1 x*lHll = 0 for allx1,…,xm A(whereEiimeansEi(x1,…,i,…,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.