Can anyone direct me to literature discussing extension fields of the form $K = \mathbb{Q}(\sqrt[4]{D})$ where $D$ is squarefree?
I'm particularly interested in results regarding the class and unit groups (and ways of computing them that are specific to such an extension field). I've tried Google, but it is of remarkably little help.
Alaca & Williams, Introductory Algebraic Number Theory, has a lot of general info on extensions, a decent amount on quadratic fields, some on cubic and quartic fields and perhaps only a very fleeting mention of quintic fields. But perhaps the bibliography might be the biggest help to you, for instance, they cite a Funakura paper for a table of integral bases and discriminants for a few quartic fields.