Local division algebras with perfect residue field of characteristic \(p>0\). (Q1174738)

Let \(k\) be a perfect field of characteristic \(p>0\). In the paper the structure of local division algebras \(D\) with residue field \(k\) is obtained. It is shown that either there exists an automorphism \(\sigma\) of \(k\) of infinite order such that \(D\) is isomorphic to the skew field of twisted power series \(k((X,\sigma))\), or \(D\) is of finite dimension over its center, \(K\), in which case it is a cyclic \(K\)-algebra.