Rings and Fields

  • David R. Finston
  • Patrick J. Morandi
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


We are all familiar with the natural, rational, real, and complex number systems and their arithmetic, but other mathematical systems exhibit similar arithmetic properties. The previous chapter, for instance, introduced the set of integers modulo n, and its addition, subtraction, and multiplication. In high school algebra you worked with polynomials, and saw how to add, subtract, and multiply them. In linear algebra you saw how arithmetic operations are performed on matrices, and might have seen vector spaces, with their addition, subtraction, and scalar multiplication. Many of the functions you studied in precalculus and calculus can be combined by addition, subtraction, multiplication, division, and also composition.


  1. 1.
    Richman F (1971) Number theory, an introduction to algebra. Brooks-Cole, MontereyzbMATHGoogle Scholar
  2. 2.
    van der Waerden BL (1971) Modern algebra. Springer, BerlinGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • David R. Finston
    • 1
    • 2
  • Patrick J. Morandi
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.CUNY Graduate CenterNew YorkUSA
  3. 3.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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