Abstract
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.
Original language | English |
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Pages (from-to) | 1577-1582 |
Number of pages | 6 |
Journal | Journal of Pure and Applied Algebra |
Volume | 218 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2014 |
ASJC Scopus subject areas
- Algebra and Number Theory