Vipul: Created page with '{{field property}} ==Definition== ===For finite extensions=== Suppose $L$ is a finite extension of a field $K$ . We say that $L$ is a '...'

2009-05-14T23:31:04Z

Created page with '{{field property}} ==Definition== ===For finite extensions=== Suppose <math>L</math> is a finite extension of a field <math>K</math>. We say that <math>L</math> is a '...'

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{{field property}}

==Definition==

===For finite extensions===

Suppose <math>L</math> is a [[finite extension]] of a [[field]] <math>K</math>. We say that <math>L</math> is a '''radical extension''' if there exist intermediate fields <math>K = K_0 \subseteq K_1 \subseteq \dots \subseteq K_r = L</math> such that each <math>K_i</math> is a [[defining ingredient::simple radical extension]] of <math>K_{i-1}</math>: In other words, each <math>K_i</math> is obtained by adjoining to <math>K_{i-1}</math> a root of a polynomial of the form <math>x^n - a</math>.

Radical extension - Revision history

Vipul: Created page with '{{field property}} ==Definition== ===For finite extensions=== Suppose L is a finite extension of a field K. We say that L is a '...'

Vipul: Created page with '{{field property}} ==Definition== ===For finite extensions=== Suppose $L$ is a finite extension of a field $K$ . We say that $L$ is a '...'