Abstract
Let A be an order integral over a valuation ring V in a central simple F-algebra, where F is the fraction field of V. We show that (a) if (Vh, Fh) is the Henselization of (V, F), then A is a semihereditary maximal order if and only if A⊗VVh is a semihereditary maximal order, generalizing the result by Haile, Morandi and Wadsworth, and (b) if J(V) is a principal ideal of V, then a semihereditary V-order is an intersection of finitely many conjugate semihereditary maximal orders; if not, then there is only one maximal order containing the V-order. 1991 Mathematics Subject Classification 16H05.
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