TY - JOUR
T1 - The Kaplansky radical of a quadratic field extension
AU - Becher, Karim Johannes
AU - Leep, David B.
PY - 2014/9
Y1 - 2014/9
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jpaa.2013.12.009
DO - 10.1016/j.jpaa.2013.12.009
M3 - Article
AN - SCOPUS:84897532770
SN - 0022-4049
VL - 218
SP - 1577
EP - 1582
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 9
ER -