REDUCED NORM MAP OF DIVISION-ALGEBRAS OVER COMPLETE DISCRETE VALUATION FIELDS OF CERTAIN TYPE

We study a ramification theory for a division algebra D of the followi ng type: The center of D is a complete discrete valuation field K with the imperfect residue field F of certain type, and the residue algebr a of D is commutative and purely inseparable over F. Using Swan conduc tors of the corresponding element of Br(K), we define Herbrand's psi-f unction of D/K, and it describes the action of the reduced norm map on the filtration of D. We also gives a relation among the Swan conduct ors and the 'ramification number' of D, which is defined by the commut ator group of D.