Extending Fields

  • Arthur Jones
  • Kenneth R. Pearson
  • Sidney A. Morris
Part of the Universitext book series (UTX)


If \({\Bbb F}\) is a subfield of ℂ and α is a complex number which is algebraic over \({\Bbb F}\), we show how to construct a certain vector space \({\Bbb F}\) (α) which contains α and which satisfies
$${\Bbb F} \subseteq {\Bbb F}\left( \alpha \right) \subseteq {\Bbb C}$$
. This vector space is then shown to be a subfield of ℂ. Thus, from the field \({\Bbb F}\) and the number α, we have produced a larger field \({\Bbb F}\)(α).


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Additional Reading for Chapter 3

  1. [AC]
    A. Clark, Elements of Abstract Algebra, Wadsworth, Belmont, California, 1971.Google Scholar
  2. [JF]
    J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.Google Scholar
  3. [WG]
    W.J. Gilbert, Modern Algebra with Applications, Wiley, New York, 1976.zbMATHGoogle Scholar
  4. [CH]
    C.R. Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs, No. 19, Mathematical Association of America, 1978.Google Scholar
  5. [LS]
    L.W. Shapiro, Introduction to Abstract Algebra, McGraw-Hill, New York, 1975.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Arthur Jones
    • 1
  • Kenneth R. Pearson
    • 1
  • Sidney A. Morris
    • 2
  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia
  2. 2.Faculty of InformaticsUniversity of WollongongWollongongAustralia

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