Abstract
We characterize the seminormality of an affine semigroup ring in terms of the dualizing complex, and the normality of a Cohen–Macaulay semigroup ring by the “shape” of the canonical module. We also characterize the seminormality of a toric face ring in terms of the dualizing complex. A toric face ring is a simultaneous generalization of Stanley–Reisner rings and affine semigroups.
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