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On additive polynomials over a finite field

Published online by Cambridge University Press:  20 January 2009

R. W. K. Odoni
R. W. K. Odoni
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
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This paper is based on the interpretation of the ring of additive polynomials in one variable over a finite field Fq, as a maximal R-order inside a certain skew-field D, R being a principal ideal domain isomorphic to Fp[T]. The classical (1930's) structure theory of maximal orders in global fields is used to solve enumeration questions involving the iteration of members of Pages from .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 1 - 16
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Chandrasekharan, K., Introduction to analytic number theory (Grundlehren, Band 148, Springer Verlag, Berlin, 1968), Ch. 8.CrossRefGoogle Scholar
2.Cohn, P. M., Algebra (volume 3) (second edition, J. Wiley & Sons, 1991), Ch. 9.Google Scholar
3.Deuring, M., Algebra (Ergebnisse der Mathematik, Band 4, Springer Verlag, Berlin, 1935).Google Scholar
4.Ireland, K. and Rosen, M., A classical introduction to modern number theory (Springer Verlag, New York, 1982), Ch. 7.CrossRefGoogle Scholar
5.Jacobson, N., Basic Algebra, (I) (W. H. Freeman and Co., U.S.A., 1974), 282–284.Google Scholar
6.Lidl, R. and Niederreiter, H., Finite fields (Encyclopaedia of Mathematics and its Applications, vol 20; Addison-Wesley, Reading, Mass., 1983), Ch. 3.Google Scholar
7.Maury, G. and Reynaud, J., Ordres maximaux au sens de K. Asano (Springer Lecture Notes in Maths., 808, 1980), Ch. V.CrossRefGoogle Scholar
8.Øre, O., On a special class of polynomials, Trans. Amer. Math. Soc. 35 (1933), 559–584; corrigendum, 36 (1934), 275.CrossRefGoogle Scholar
9.Øre, O., Theory of non-commutative polynomials, Ann. of Maths. 34 (1933), 480–508.CrossRefGoogle Scholar
10.Reiner, I., Maximal Orders (Academic Press, London, 1975).Google Scholar
11.Schilling, O. F. G., The Theory of Valuations (Amer. Math. Soc., New York, 1950), 57, 101.CrossRefGoogle Scholar
12.Wilkerson, C., A primer on the Dickson invariants, Contemp. Math. 19 (1983), 421–434.CrossRefGoogle Scholar