Category:Definitions/Class Groups
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This category contains definitions related to Class Groups.
Related results can be found in Category:Class Groups.
Let $F$ be a field of algebraic numbers.
Let $H$ be the set of ideals of the elements of $F$.
Let $\RR$ be the equivalence relation on $H$ defined as:
- $\forall I, J \in H: I \mathrel \RR J \iff \exists S, T, \in H: I S = J T$
where $S$ and $T$ are principal ideals of $F$.
Let $G$ be the group of equivalence classes of $\RR$ such that the group operation is that the product of the equivalence classes containing $I$ and $J$ is the equivalence class containing $I J$.
This group is known as the class group of $F$.
Pages in category "Definitions/Class Groups"
The following 3 pages are in this category, out of 3 total.