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Permutation polynomials in several variables over residue class rings

Part of: Ring extensions and related topics

Published online by Cambridge University Press:  09 April 2009

H. K. Kaiser  and
W. Nöbauer
H. K. Kaiser
Affiliation:
Institut für Algebra und Diskrete Mathematik Technische Universität WienWiedner Hauptstraße 8–10 A-1040 Vienna, Austria
W. Nöbauer
Affiliation:
Institut für Algebra und Diskrete Mathematik Technische Universität WienWiedner Hauptstraße 8–10 A-1040 Vienna, Austria
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Abstract

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The concept of a permutation polynomial function over a commutative ring with 1 can be generalized to multiplace functions in two different ways, yielding the notion of a k-ary permutation polynomial function (k > 1, k ∈ N) and the notion of a strict k-ary permutation polynomial function respectively. It is shown that in the case of a residue class ring Zm of the integers these two notions coincide if and only if m is squarefree.

MSC classification

Secondary: 13B25: Polynomials over commutative rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 171 - 175
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Lausch, H. and Nöbauer, W., Algebra of polynomials (North-Holland, Amsterdam, 1973).Google Scholar
[2]Lidl, R. and Niederreiter, H., Finite fields (Addison-Wesley, Reading, Massachusetts, 1983).Google Scholar
[3]Nöbauer, W., ‘Darstellung von Permutationen durch Polynome und rationale Funktionen’, Berichte des Math. Forschungsinst. Oberwolfach 5 (1971), 89–100.Google Scholar