The radical of a field consists of all nonzero elements that are represented by every binary quadratic form representing 1. Here, the radical is studied in relation to local-global principles, and further in its behavior under quadratic field extensions. In particular, an example of a quadratic field extension is constructed where the natural analogue to the square-class exact sequence for the radical fails to be exact. This disproves a conjecture of Kijima and Nishi.
|Number of pages||6|
|Journal||Journal of Pure and Applied Algebra|
|State||Published - Sep 2014|
ASJC Scopus subject areas
- Algebra and Number Theory