Irreducible Polynomials

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


In our earlier definition of the irreducible polynomial of a number, the word “irreducible” was intended to convey the idea that the degree of the polynomial “could not be reduced further”. In this chapter it will be shown that this polynomial is also “irreducible” in the sense that it “cannot be factorized further”. This will lead to a practical technique for finding the irreducible polynomial of a number.


Extension Field Irreducible Polynomial Abstract Algebra Early Definition Division Theorem 
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Additional Reading for Chapter 4

  1. [CA]
    Computer Algebra: Symbolic and Algebraic Computation, ed. B. Buchberger, G.E. Collins, R. Loos and R. Albrecht, Springer, Vienna, 2nd edition, 1983.Google Scholar
  2. [AC]
    A. Clark, Elements of Abstract Algebra, Wadsworth, Belmont, California, 1971.Google Scholar
  3. [JF]
    J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.Google Scholar
  4. [WG]
    W.J. Gilbert, Modern Algebra with Applications, Wiley, New York, 1976.zbMATHGoogle Scholar
  5. [CH]
    C.R. Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs, No. 19, Mathematical Association of America, 1978.Google Scholar
  6. [HH]
    H. Holden, “Rings on ℝ2”, Mathematics Magazine, 62 (1989), 48–51.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [IH]
    I.N. Herstein, Topics in Algebra, Blaisdell, New York, 1964.zbMATHGoogle Scholar
  8. [LS]
    L.W. Shapiro, Introduction to Abstract Algebra, McGraw-Hill, New York, 1975.zbMATHGoogle Scholar
  9. [MS]
    M. Spivak, Calculus, W.A. Benjamin, New York, 1967.zbMATHGoogle Scholar
  10. [RY]
    R.M. Young, “When is ℝn a field?”, The Mathematical Gazette, 72 (1988), 128–129.MathSciNetCrossRefGoogle 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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