Abstract
A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Römer 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 square-free module theory over R, and show that the Cohen-Macaulay, Buchsbaum, and Gorenstein* properties of R are topological properties of its associated cell complex.
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