2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168098A "toric face ring", which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Roemer and their coauthors recently. In this paper, under the "normality" assumption, we describe a dualizing complex of a toric face ring $R$ in a very concise way. Since $R$ is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory over $R$, and show that the Buchsbaum property and the Gorenstein* property of $R$ are topological properties of its associated cell complex.22 pagesCommutative Algebra13F55; 13D25text