Kaplansky Radical
The Hilbert symbol on a field F defines a map
where Br(F) is the Brauer group of F. The kernel of this mapping, the elements a such that (a,b)=1 for all b, is the Kaplansky radical of F.
The radical is a subgroup of F*/F*2, identified with a subgroup of F*. The radical contains is equal to F* if and only if F is not formally real and has u-invariant at most 2.
Read more about this topic: Hilbert Symbol
Famous quotes containing the word radical:
“A radical is a man with both feet firmly planted in the air. A conservative is a man with two perfectly good legs, who, however, has never learned to walk forward. A reactionary is a somnambulist walking backwards. A liberal is a man who uses his legs and his hands at the behest ... of his head.”
—Franklin D. Roosevelt (1882–1945)