Perfect Field
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In field theory, a branch of algebra, a field k is said to be perfect if any one of the following equivalent conditions holds: Every irreducible polynomial over k has distinct roots. Every polynomial over k is separable. Every finite extension of k is separable. Either k has characteristic 0, or, when k has characteristic p 0, every element of k is a pth power. Every element of k is a qth power. (Here, q is the characteristic exponent, equal to 1 if k has…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In field theory, a branch of algebra, a field k is said to be perfect if any one of the following equivalent conditions holds: Every irreducible polynomial over k has distinct roots. Every polynomial over k is separable. Every finite extension of k is separable. Either k has characteristic 0, or, when k has characteristic p 0, every element of k is a pth power. Every element of k is a qth power. (Here, q is the characteristic exponent, equal to 1 if k has characteristic 0, and equal to p if k has characteristic p 0). The separable closure of k is algebraically closed.