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Algebra pp 118-156 | Cite as

Rings: Polynomials and factorization

  • L. E. Sigler
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

We begin with the properties of polynomials found in school algebra and then move in Section 5.2 to a relatively formal construction of the polynomial ring. Particularly interesting to students ought to be the altered properties of polynomials when the ring of coefficients is not a field. Section 5.3 deals with polynomial functions arising from polynomials emphasizing the distinction between these two concepts. Although this is a small point to a professional mathematician, an understanding of such distinctions helps mature the student of mathematics. The matters at stake in the factor theorem are then clearer. We are then led to the important results counting the number of roots of a polynomial and the concept of multiplicity of roots.

Keywords

Polynomial Function Prime Ideal Commutative Ring Integral Domain Polynomial Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, Inc. 1976

Authors and Affiliations

  • L. E. Sigler
    • 1
  1. 1.Department of MathematicsBucknell UniversityLewisburgUSA

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