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Groups and Fields: The Two Fundamental Notions of Algebra

  • James B. CarrellEmail author
Chapter

Abstract

Algebra is the mathematical discipline that arose from the problem of solving equations. If one starts with the integers \({\mathbb Z}\), one knows that every equation \(a+x=b\), where a and b are integers, has a unique solution. However, the equation \(ax=b\) does not necessarily have a solution in \({\mathbb Z}\), or it might have infinitely many solutions (take \(a=b=0\)).

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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