Totally ramified valuations on finite-dimensional division algebras
Totally ramified valuations on finite-dimensional division algebras
Division algebras $D$ with valuation $v$ are studied, where $D$ is finite-dimensional and totally ramified over its center $F$ (i.e., the ramification index of $v$ over $v{|_F}$ equals $[D:F]$). Such division algebras have appeared in some important constructions, but the structure of these algebras has not been systematically analyzed before. …