Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

Abstract

Regarding polynomial functions on a subset S of a non-commutative ring R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coefficients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R [x].