Narrow Results

Let A be a finitely generated commutative algebra over a field K with a presentation A = K 〈X₁,…, X_n | R〉, where R is a set of monomial relations in the generators X₁,…, X_n. So A = K[S], the semigroup algebra of the monoid S = 〈X₁,…, X_n | 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.