Polynomial functions in the residue class rings of Dedekind domains

Abstract

In this paper, as an extension of the integer case, we define polynomial functions over the residue class rings of Dedekind domains, and then we give canonical representations and counting formulas for such polynomial functions. In particular, we give an explicit formula for the number of polynomial functions over the residue class rings of polynomials over finite fields.

15 pages

References in corpus (2)

• Congruence preserving functions in the residue class rings of polynomials over finite fields
• Gauss factorials of polynomials over finite fields

Cited by in corpus (4)

• The Ring of Polyfunctions over $\mathbb{Z}/n\mathbb{Z}$
• Polynomial analogue of the Smarandache function
• Congruence preserving functions in the residue class rings of polynomials over finite fields
• A proof of Sondow's conjecture on the Smarandache function