On Centralizer-Related Intermediate Fields of a Skew Field Extension

For a skew field extension L/K, a number of intermediate fields can be defined on the basis of the centralizer of K in L. In this paper such intermediate fields are studied in detail. Among the results are a standard decomposition of any skew field extension of finite degree and four types of skew field extensions that are basic to such a standard decomposition. A number of persistence properties of these types are explored.