Perfect field

In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds:

Otherwise, k is called imperfect.

In particular, all fields of characteristic zero and all finite fields are perfect.

Perfect fields are significant because Galois theory over these fields becomes simpler, since the general Galois assumption of field extensions being separable is automatically satisfied over these fields (see third condition above).

单词	Imperfect field
释义	Imperfect field 英语百科 Perfect field In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds: Otherwise, k is called imperfect. In particular, all fields of characteristic zero and all finite fields are perfect. Perfect fields are significant because Galois theory over these fields becomes simpler, since the general Galois assumption of field extensions being separable is automatically satisfied over these fields (see third condition above).
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Imperfect field

Perfect field