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On a Result in Polynomial Rings
Published online by Cambridge University Press: 24 October 2008
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.
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- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 104 - 108
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- Copyright © Cambridge Philosophical Society 1960