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Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

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16

Selected Applications of Galois Theory

In this chapter, we discuss certain important applications of Galois theory to classical problems. The first is the fundamental theorem of algebra which states that any polynomial over the field of complex numbers ℂ has all the roots in ℂ which is equivalent to saying that any polynomial over ℂ can be factored completely into linear factors over ℂ. We prove this by using various techniques of Galois theory. Also we discuss problems of finding solutions of polynomial equations (that is, finding roots of polynomials) by radicals; that is, expressing ...

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