2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73306Let $Δ$ be a stable simplicial complex on $n$ vertexes. Over an arbitrary base field $K$, the symmetric algebraic shifted complex $Δ^s$ of $Δ$ 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 $Δ$ are equal.9 pagesCommutative Algebra13F55; 13D02; 55U10text