Amitsur complex (original) (raw)

In algebra, the Amitsur complex is a natural complex associated to a ring homomorphism. It was introduced by Shimshon Amitsur. When the homomorphism is faithfully flat, the Amitsur complex is exact (thus determining a resolution), which is the basis of the theory of faithfully flat descent. The notion should be thought of as a mechanism to go beyond the conventional localization of rings and modules.