Abstract
We begin with the geometric problem of constructions with ruler and compass. We then introduce the notions of fields, of field extensions, and of algebraic extensions. This will quickly give us the key to the impossibility of some classical problems. In Chapter 5 we will be able to see how Galois theory gives a definitive criterion allowing us to decide if a geometric construction is, or is not, feasible with ruler and compass.
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© 2005 Springer Science+Business Media, Inc.
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(2005). Field extensions. In: A Field Guide to Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/0-387-26955-X_1
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DOI: https://doi.org/10.1007/0-387-26955-X_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-21428-3
Online ISBN: 978-0-387-26955-9
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