Integral Semihereditary Orders inside a Bézout Maximal Order Original Research Article

In this paper we show that over a commutative valuation ringV, a semihereditaryV-orderHin a finite-dimensional simple Artinian ring is a (finite) intersection of Bézout (maximal)V-orders iff eitherHis Bézout orHis contained in a BézoutV-order andJ(V) is a principal ideal ofV.