Ideal Class Group - Examples of Ideal Class Groups

Examples of Ideal Class Groups

  • The rings Z, Z, and Z, where ω is a cube root of 1 and i is a fourth root of 1 (i.e. a square root of −1), are all principal ideal domains, and so have class number 1: that is, they have trivial ideal class groups.
  • If k is a field, then the polynomial ring k is an integral domain. It has a countably infinite set of ideal classes.

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