  Let $\Delta$ be a stable simplicial complex on $n$ vertexes. Over an
arbitrary base field $K$, the symmetric algebraic shifted complex $\Delta^s$ of
$\Delta$ is defined. It is proved that the Betti numbers of the Stanley-Reisner
ideals in the polynomial ring $K[x_1,x_2,...,x_n]$ of the symmetric algebraic
shifted, exterior algebraic shifted and combinatorial shifted complexes of
$\Delta$ are equal.
