Basics of Ring Theory

  • Joseph L. Awange
  • Béla Paláncz


This chapter presents the concepts of ring theory from a geodetic and geoinformatics perspective. The presentation is such that the mathematical formulations are augmented with examples from the two fields. Ring theory forms the basis upon which polynomial rings operate. As we shall see later, exact solution of algebraic nonlinear systems of equations are pinned to the operations on polynomial rings. In Chap.  3, polynomials will be discussed in detail. In order to understand the concept of polynomial rings, one needs first to be familiar with the basics of ring theory. This chapter is therefore a preparation for the understanding of the polynomial rings presented in Chap.  3. Ring of numbers which is presented in Sect. 2.2 plays a significant role in daily operations. They permit operations addition, subtraction, multiplication and division of numbers. For those engaged in data collection, ring of numbers play the following role;
  • they specify the number of sets of observations to be collected,

  • they specify the number of observations or measurements per set,

  • they enable manipulation of these measurements to determine the unknown parameters.


Natural Number Geographical Information System Rational Number Polynomial Ring Ring Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Joseph L. Awange
    • 1
  • Béla Paláncz
    • 2
  1. 1.Curtin UniversityPerthAustralia
  2. 2.Budapest University of Technology and EconomicsBudapestHungary

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