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On a Result in Polynomial Rings

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
Trinity CollegeCambridge
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Extract

Let denote the polynomial algebra over the integers in countably many variables ui (i ≥ 1). Let ∂ be the derivation of defined on the generators by. Thus if is graded by dim ui=i, then∂ is homogeneous, of degree − 1. The result is that ∂ is onto, and that its kernel is a polynomial algebra in , where is homogeneous of degree i and the coefficient of ui in is p if i is a power of a prime p, and 1 if i is not a prime power.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 104 - 108
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

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