  In this short note, we give a characterization of domains satisfying Serre's
condition $(\mathrm{R}_1)$ in terms of their canonical modules. In the special
case of toric rings, this generalizes a result of the second author (K.
Yanagawa, Dualizing complexes of seminormal affine semigroup rings and toric
face rings, J. Algebra 425 (2015).) where the normality is described in terms
of the "shape" of the canonical module.
