  We define a variant of normal basis, called a {\em Galois scaffolding}, that
allows for an easy determination of valuation, and has implications for Galois
module structure. We identify fully ramified, elementary abelian extensions of
local function fields of characteristic $p$, called {\em one-dimensional},
that, in a particular sense, are as simple as cyclic degree $p$ extensions, and
prove the statement in the title above.
