SUMS OF CORESTRICTIONS OF CYCLIC ALGEBRAS

By a cyclic layer of a finite Galois extension, E/K, of fields one mea ns a cyclic extension, L/F, of fields where E superset of or equal to L superset of F superset of or equal to K. Let C(E/K) denote the subgr oup of the relative Brauer group, Br(E/K), generated by the various su bgroups cor(Br(L/F)) as L/F ranges over all cyclic layers of E/K and w here cor denotes the corestriction map into Br(E/K). We show that for K global, [Br(E/K) : C(E/K)] < infinity and we produce examples where C(E/K) not equal Br(E/K).