BRAUER GROUP OVER A KRULL DOMAIN

Let R be a Krull domain with field of fractions K. By Br(R) we denote the Brauer group of R. Studying the Kernel of the homomorphism Br(R).rarw.Br(K), Orzech defined Brauer groups Br(M) for different categories M of R-modules [4]. In this paper we show that an algebra A in Br(D) is a maximal order in A K and that the map Br(D).rarw. Br(K) is one to one. We note here few conventions. All rings are Krull domains and all modules will be unitary. By Z we donote the set of height one prime ideals of a Krull domain.