On a class of infinite rings

Abstract

Let α1,... ,αn ∈ ℕ. We prove that, in every infinite ring R, x1α1 ⋯xnαn = 0 for all x1,..., xn ∈ R if and only if, for any n infinite subsets X1,..., Xn of R, there exist x1 ∈ X1, ..., xn ∈ Xn such that x1α1 ⋯ xnαn = 0. © Inst. Math. CAS 2001.