Review of Applied Algebra

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


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.


Finite Field Unit Group Polynomial Ring Great Common Divisor Quotient Ring 
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  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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