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

2018/09/24 by Frisch, Sophie
#13F20 #16D25 #16P10 #16S99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1809.09160

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].

Related

• Polynomial functions on a class of finite non-commutative rings
• Polynomial functions on upper triangular matrix algebras
• The Ideal of Vanishing Polynomials and the Ring of Polynomial Functions
• Polynomial in Non-Commutative Algebra
• Value sets of non-permutation polynomials over the residue class rings of integers