On functional identities and d-free subsets of rings, I

Abstract

LetA be a prime ring with maximal right ring of quotients Q and with extended centroid C. Further, let S be a set, let αS→ A be a map, let m be a positive integer and let E_i F_i S ^m-1, be maps. We study functional identities of the form for all s ₁,s ₂,⋯,s_m ϵ S (where , etc). If S^α is an (m+ l)-free subset of Q (for example, if S ^α = A and A is not algebraic of bounded degree m+1 over C, or S ^α is a ncentral Lie ideal of A and A is not algebraic of bounded degree m + 2 over C), definitive results are obtained.

1991 Mathematics Subject Classification:

• Primary: 16W25
• Secondary: 16R50