### Abstract

Let R = GR(p^{n}, m) denote the Galois ring of order p^{nm} where p is a prime and n, m ≥ 1 are integers. In this paper, the authors derive formulas for the total number of functions from R to itself which can be represented by polynomials over R and they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod p^{n}.

Original language | English (US) |
---|---|

Pages (from-to) | 156-166 |

Number of pages | 11 |

Journal | Journal of Number Theory |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1992 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*41*(2), 156-166. https://doi.org/10.1016/0022-314X(92)90116-7

}

*Journal of Number Theory*, vol. 41, no. 2, pp. 156-166. https://doi.org/10.1016/0022-314X(92)90116-7

**Functions and polynomials over Galois rings.** / Brawley, Joel V.; Mullen, Gary Lee.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Functions and polynomials over Galois rings

AU - Brawley, Joel V.

AU - Mullen, Gary Lee

PY - 1992/1/1

Y1 - 1992/1/1

N2 - Let R = GR(pn, m) denote the Galois ring of order pnm where p is a prime and n, m ≥ 1 are integers. In this paper, the authors derive formulas for the total number of functions from R to itself which can be represented by polynomials over R and they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pn.

AB - Let R = GR(pn, m) denote the Galois ring of order pnm where p is a prime and n, m ≥ 1 are integers. In this paper, the authors derive formulas for the total number of functions from R to itself which can be represented by polynomials over R and they also derive a formula for the number of such permutations of R. These results not only generalize but unify into a single theory, known results for finite fields and the integers mod pn.

UR - http://www.scopus.com/inward/record.url?scp=38249011843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249011843&partnerID=8YFLogxK

U2 - 10.1016/0022-314X(92)90116-7

DO - 10.1016/0022-314X(92)90116-7

M3 - Article

AN - SCOPUS:38249011843

VL - 41

SP - 156

EP - 166

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -