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Number Fields pp 130-157 | Cite as

The ideal class group and the unit group

  • Daniel A. Marcus
Part of the Universitext book series (UTX)

Abstract

Recall that the ideal class group of a number ring R consists of equivalence classes of nonzero ideals under the relation
$$ I\sim J\quad iff\quad \alpha I = \beta J\quad for{\text{ }}some{\text{ }}non{\text{ }}zero{\text{ }}\alpha ,\beta \in R; $$
the group operation is multiplication defined in the obvious way, and the fact that this is actually a group was proved in chapter 3 (Corollary 1 of Theorem 15). In this chapter we will prove that the ideal class group of a number ring is finite and establish some quantitative results that will enable us to determine the ideal class group in specific cases.

Keywords

Unit Group Prime Divisor Free Abelian Group Ideal Class Fundamental Unit 
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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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Daniel A. Marcus
    • 1
  1. 1.Department of MathematicsCalifornia State Polytechnic UniversityPomonaUSA

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