Polynomial functions on 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 $R[x]$.

arXiv comment9 pages, conference paper for "advances in algebra ..." at Ton Duc Thang University, Vietnam, Dec 18-20, 2018

References in corpus (2)

• Integer-valued polynomials on algebras
• Decomposition of integer-valued polynomial algebras