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radical∗
Wkbj79†
2013-03-21 22:32:25
Let F be a field and α be algebraic over F . Then α is a radical over F if
there exists a positive integer n with αn ∈ F .
Note that, if K/F is a field extension and α is a radical over F , then α is
automatically a radical over K.
Following are some examples of radicals:
r
a
1. All numbers of the form n , where n is a positive integer and a and b
b
are integers with b 6= 0 are radicals over Q.
√
√
√
√
√
2. The number 4 2 is a radical over Q( 2) since ( 4 2)2 = 2 ∈ Q( 2).
∗ hRadical1i created: h2013-03-21i by: hWkbj79i version: h39190i Privacy setting: h1i
hDefinitioni h12F05i h12F10i
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