Construction Problems and Field Extensions

  • Robin Hartshorne
Part of the Undergraduate Texts in Mathematics book series (UTM)


During the earlier parts of this book, we started always from Euclid’s geometry, developing and expanding it using our modern mathematical awareness. Because of the construction of the field of segment arithmetic, one could even argue that the use of fields in Chapter 4 arises naturally from the geometry. In this chapter, however, we will make use of modern algebra, the theory of equations and field extensions, and in particular the Galois theory, as it developed in the late nineteenth and early twentieth centuries.


Real Root Galois Group Field Extension Minimal Polynomial Galois Theory 
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Copyright information

© Robin Hartshorne 2000

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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