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Review of Applied Algebra

  • Richard Tolimieri
  • Chao Lu
  • Myoung An
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)

Abstract

In this chapter we will give a brief account of several important results from applied algebra necessary to develop the algorithms in this text. In particular, we will describe the main properties of the following rings:
  • • Ring of integers Z.

  • • Quotient ring Z/N of integers modulo N.

  • • Ring of polynomials F[x] over the field F.

  • • Quotient ring F[x]/f(x) of polynomials.

Keywords

Finite Field Unit Group Polynomial Ring Great Common Divisor Quotient 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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References

  1. [1]
    Ireland, K. and Rosen, M. A Classical Introduction to Modern Number Theory, Springer-Verlag, 1980.Google Scholar
  2. [2]
    Halmos, P. R. Finite-Dimensional Vector Spaces, Springer-Verlag, 1974.Google Scholar
  3. [3]
    Herstein, I. N. Topics in Algebra, XEROX College Publishing, 1964.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Richard Tolimieri
    • 1
  • Chao Lu
    • 2
  • Myoung An
    • 3
  1. 1.Department of Electrical EngineeringCity College of CUNYNew YorkUSA
  2. 2.Department of Computer and Information SciencesTowson State UniversityTowsonUSA
  3. 3.A.J. Devaney AssociatesAllstonUSA

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