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Field Extensions

In: Quintic Equations and How to Solve Them

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  • C. M. Linton

Abstract

In Sect. 3.1 we introduced the concept of a field, a set of numbers which allows us to perform the operations of addition, subtraction, multiplication and division (except by zero) without leaving the set. When finding the roots of polynomials we need to extract roots: square roots, cube roots and so on, and these operations are not included in the definition of a field.

Suggested Citation

  • C. M. Linton, 2025. "Field Extensions," Springer Books, in: Quintic Equations and How to Solve Them, chapter 5, pages 55-65, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-01658-4_5
    DOI: 10.1007/978-3-032-01658-4_5
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