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Some arithmetical functions in finite fields

Published online by Cambridge University Press:  18 May 2009

Stephen D. Cohen
Stephen D. Cohen
Affiliation:
University of Glasgow, Glasgow, W.2.
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In this paper, we investigate various “arithmetical” functions associated with the factorisation of polynomials in GF[q, X1, …, Xk], where k ≥ 1 and GF[q]is the finite field of order q. We shall assume throughout that all polynomials discussed are non-zero and have been normalised by selecting one polynomial from each equivalence class with respect to multiplication by non-zero elements of GF[q]. The constant polynomial will be denoted by 1. With this normalisation, GF[q, X1, …, Xk] becomes a unique factorisation domain. When k = 1, normalisation is achieved by considering only monic polynomials. By the degree of a polynomial A(X1, …, Xk) will be understood the ordered set (m1, …, mk), where m1 is the degree of A(X1, …, Xk) in X1,(i = 1, …, k).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 1 , January 1970 , pp. 21 - 36
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

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