Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:07:55.579Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bott, R., The stable homotopy of the classical groups. Proc. Nat. Acad. Sci., Wash., 43 (1957), 933–5.Google Scholar
(2)Steenrod, N. E., and Whitehead, J. H. C., Vector fields on the n-sphere. Proc. Nat. Acad. Sci., Wash. 37 (1951), 58–63.Google Scholar