On seminormality

We give an elementary and essentially self-contained proof that a reduced ring R is seminormal if and only if the canonical map is an isomorphism, a theorem due to Swan [R. Swan, On seminormality, J. Algebra 67 (1980) 210–229], generalizing some previous results of Traverso [C. Traverso, Seminormality and the Picard group, Ann. Scuola Norm. Sup. Pisa 24 (1970) 585–595].