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?