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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.
KeywordsExtension Field Irreducible Polynomial Abstract Algebra Early Definition Division Theorem
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Additional Reading for Chapter 4
- [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
- [AC]A. Clark, Elements of Abstract Algebra, Wadsworth, Belmont, California, 1971.Google Scholar
- [JF]J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.Google Scholar
- [CH]C.R. Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs, No. 19, Mathematical Association of America, 1978.Google Scholar