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Functions and polynomials over finite commutative rings

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Summary.

Let R be a finite commutative ring. In this paper, the authors derive an upper bound for the total number of functions from R to itself which can be represented by polynomials over R. A necessary condition on R for the upper bound to be obtained is also provided. These results generalize known results for Galois rings.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A., e-mail: cjmaxson@math.tamu.edu, , , , , , US

    C. J. Maxson

  2. Department of Mathematics, University of Stellenbosch, 7600 Stellenbosch, South Africa, e-mail: abvdm@land.sun.ac.za, , , , , , ZA

    A. B. van der Merwe

Authors
  1. C. J. Maxson
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  2. A. B. van der Merwe
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Received: February 23, 1999.

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Maxson, C., van der Merwe, A. Functions and polynomials over finite commutative rings. Aequ. math. 62, 30–38 (2001). https://doi.org/10.1007/PL00000141

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  • DOI: https://doi.org/10.1007/PL00000141

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