On Roberts rings

In 1985, P. C. Roberts [14] proved the vanishing theorem of intersection mu ltiplicities fur a local ring that satisfies tau (A/S)([A])= [SpecA](dim A) , where tau (A/S) is the Riemann-Roch map for SpecA with regular base schem e SpecS. We refer such rings as Roberts rings. For rings of positive charac teristic, we can characterize Roberts rings by the Frobenius maps. For ring s with field of fractions of characteristic 0, we can characterize Roberts rings by some Galois extensions. We shall give basic properties and example s of Roberts rings in the paper.