Bézout Orders and Henselization Original Research Article

Let B be a Bézout maximal order over a valuation ring V in a central simple F-algebra S. If (Fh, Vh) is the Henselization of (F, V) then the main result of this paper is that B circle times operatorVVh is a maximal Vh-order in S circle times operatorFFh. Furthermore we show that this maximal order is semihereditary (but not Bézout in general) and that certain numerical invariants of B considered by Wadsworth and Gräter readily show up in the structure of B circle times operatorV, Vh.