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I'm confused about a terminology.

In Frank W. Warner's book Foundations of Differentiable Manifolds and Lie Groups, it says on page 12

Let $F_m$, a subset of $\bar{F_m}$ (the set of germs at $m$), be the set of germs which vanish at m. Then $F_m$ is an ideal in $\bar{F_m}$, and we let $F_m^k$ denote its kth power. $F_m^k$ is the ideal of $\bar{F_m}$ consisting of all finite linear combinations of k-fold products of elements of $F_m$.

Is an ideal this thing?

What does it mean to take the $k$th power of an ideal?

  • 0
    Warner has a manifold? :) You should probably mention the name by its correct title.2012-05-08
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    *Ideal* is used there in the sense of ring theory.2012-05-08
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    A few lines before, he says The operations of addition, scalar multiplication, and multiplication of functions induce on F_m tilda the structure of an algebra over $\mathbb R.$2012-05-08
  • 1
    Thanks! I guess ring theory is a prerequisite.2012-05-08
  • 0
    See Wikipedia: http://en.wikipedia.org/wiki/Ideal_(ring_theory)2012-05-08

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