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A generalization of a theorem on the content of polynomials

Published online by Cambridge University Press:  24 October 2008

D. G. Northcott
D. G. Northcott
Affiliation:
The University Sheffield
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Extract

Introduction. By the content of a polynomial with coefficients in a ring R, one understands either the R-ideal or (better) the additive group which the coefficients generate. There are important connexions between the contents of two polynomials and the content of their product, and results of this kind are to be found in the work of Gauss. Here we shall give a wide generalization of a theorem of this type not involving polynomials at all; however, as the reader will observe, the proof is essentially a reduction to the polynomial case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 4 , October 1959 , pp. 282 - 288
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

† Note that the concepts (M, G)-set, (R, G)-set and G-product extend at once to situations in which G is only a semi-group.

† I have not been able to find a reference for Lemma l and so a proof has been supplied in the appendix. This proof was given by E. Artin in a lecture at Princeton University some years ago.