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Erschienen in:
2019 | OriginalPaper | Buchkapitel
7. Field Extensions
verfasst von : Matej Brešar
Erschienen in: Undergraduate Algebra
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Abstract
This last chapter is the closest to the origin of algebra. Field extensions are intimately connected with polynomial equations, the subject of investigation of classical algebra. In the first section, we present a historical overview which should help the reader to better understand the content of this chapter, and, in fact, of the whole book. The theory developed in subsequent sections is mathematically rich with several impressive results, culminating in Galois theory, which, along with its applications, often strikes mathematical souls with its harmony and perfection.