Factorization in hereditary orders (Q1177251)

Let \(\Lambda\) be a hereditary order in a central separable algebra \(A\) over a global field, such that the Eichler condition is satisfied. The author proves that for \(\lambda\in\Lambda\), \(r\in R\), with \(r\mid nr(\lambda)\), there exist \(u\in R^*\) and a left divisor \(\rho\in\Lambda\) for \(\lambda\) such that \(nr(\rho)=ru\). If \(A\) is a matrix algebra, it follows that \(\lambda\in\Lambda\) has a right divisor with determinant \(r\in R\) whenever \(r\mid \det \lambda\).