Polynomial functions in the residue class rings of Dedekind domains

Xiumei Li; Min Sha

doi:10.1142/S1793042119500854

Polynomial functions in the residue class rings of Dedekind domains

Xiumei Li, Min Sha^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1473-1486
Number of pages	14
Journal	International Journal of Number Theory
Volume	15
Issue number	7
DOIs	https://doi.org/10.1142/S1793042119500854
Publication status	Published - Aug 2019

Keywords

Dedekind domain
finite field
Polynomial function
residue class ring

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10.1142/S1793042119500854

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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.",

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author = "Xiumei Li and Min Sha",

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T1 - Polynomial functions in the residue class rings of Dedekind domains

AU - Li, Xiumei

AU - Sha, Min

PY - 2019/8

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N2 - 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.

AB - 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.

KW - Dedekind domain

KW - finite field

KW - Polynomial function

KW - residue class ring

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DO - 10.1142/S1793042119500854

M3 - Article

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SP - 1473

EP - 1486

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 7

ER -

Polynomial functions in the residue class rings of Dedekind domains

Abstract

Keywords

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