The Theorem Of The Primitive Element

Daniel H. Ullman, Daniel J. Velleman,Douglas B. West,Paul Bracken, Ezra A. Brown,Zachary Franco,George Gilbert,Laszlo Liptak, Rick Luttmann,Hosam Mahmoud, Frank B. Miles, Lenhard Ng, Rajesh Pereira, Kenneth Stolarsky,Richard Stong,Stan Wagon,Lawrence Washington,Li Zhou

American Mathematical Monthly（2021）

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摘要

The theorem of the primitive element is one of the basic results of Galois theory. We present a proof, different from the standard one, that is undoubtedly not new, but which in our opinion deserves to be better known. We also show how to find a primitive element in an important special case, a result which does not appear in the standard texts, and which in our opinion deserves to be much better known.

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