Crossed product and hereditary orders (Q1073095)

Let L/K be a finite Galois extension of local fields and let d, e, and f be the different exponent, ramification index, and inertial degree of L/K. For a certain crossed product order \(\wedge\) over K the authors prove that a specified last order \(\wedge_ s\) in a chain is the unique minimal hereditary order in \(A=K\wedge\) containing \(\wedge\), that \(\wedge_ s\) has e/m simple modules (where m is the Schur index of A), each of dimension f over the residue class field of the ring of integers of K, and that \(s=d-(e-1)\).