Normal Domains with Monomial Presentations

Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . , Xn | R〉, where R is a set of monomial relations in the generators X1, . . . , Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1, . . . , Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relations. Also the class group of such algebras A is calculated. Mathematics Subject Classification 2000: primary 16S36, 13B22; secondary 14M25, 16H05, 13C20, 20M14 keywords: normal domain, class group, finitely presented algebra, semigroup algebra, commutative semigroup, normal semigroup