Title

Everywhere vanishing polynomial functions

Article Type

Research Article

Publication Title

Journal of Algebra and its Applications

Abstract

If R is a finite commutative ring, it is well known that there exists a nonzero polynomial in R[T] which is satisfied by every element of R. In this paper, we class ify all commutative rings R such that every element of R satisfies a particular monic polynomial. If the polynomial, satisfied by the elements of R, is not required to be monic, then we can give a classification only for Noetherian rings, giving examples to show that the characterization does not extend to arbitrary commutative rings.

DOI

10.1142/S0219498820500395

Publication Date

1-1-2019

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