Abstract
Recall the two major questions that we had posed to ourselves in Chapter 4. If K/F is a field extension and a is an element of K, we were wondering whether there is some property of a that would determine whether F[a] = F(a), and we were wondering what the relation is between the element a and the degree of F(a) over F. We had alluded to the minimal polynomial of a over F, but we had to delay discussing this concept until we had first studied polynomials.
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© 1997 Springer Science+Business Media New York
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Sethuraman, B.A. (1997). The Field Generated by an Element. In: Rings, Fields, and Vector Spaces. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2700-5_7
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DOI: https://doi.org/10.1007/978-1-4757-2700-5_7
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