  The non-local conserved quantities of N=1 Super KdV are obtained using a
complete algebraic framework where the Gardner category is introduced. A
fermionic substitution semigroup and the resulting Gardner category are defined
and several propositions concerning their algebraic structure are proven. This
algebraic framework allows to define general transformations between different
nonlinear SUSY differential equations. We then introduce a SUSY ring extension
to deal with the non-local conserved quantities of SKdV. The algebraic version
of the non-local conserved quantities is solved in terms of the exponential
function applied to the $D^{-1}$ of the local conserved quantities of SKdV.
Finally the same formulas are shown to work for rapidly decreasing superfields.
