The Kaplansky radical of a quadratic field extension

Karim Johannes Becher, David B. Leep

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1577-1582
Number of pages6
JournalJournal of Pure and Applied Algebra
Issue number9
StatePublished - Sep 2014

ASJC Scopus subject areas

  • Algebra and Number Theory


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