Splitting 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 abstract algebra, the splitting field of a polynomial P(X) over a given field K is a field extension L of K over which P factorizes ("splits", hence the name of a splitting field) into linear factors X ai, and such that the ai generate L over K. The extension L is then an extension of minimal degree over K in which P splits. It can be shown that such splitting fields exist, and are unique up to isomorphism; the amount of freedom in that isomorphism is known to be…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 abstract algebra, the splitting field of a polynomial P(X) over a given field K is a field extension L of K over which P factorizes ("splits", hence the name of a splitting field) into linear factors X ai, and such that the ai generate L over K. The extension L is then an extension of minimal degree over K in which P splits. It can be shown that such splitting fields exist, and are unique up to isomorphism; the amount of freedom in that isomorphism is known to be the Galois group of P (if we assume it is separable). For an example if K is the rational number field Q and P(X) = X3 2, then a splitting field L will contain a primitive cube root of unity, as well as a cube root of 2.