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See Also: existence of Hilbert class field, fractional ideal, number field, unramified extensions and class number divisibility, class number divisibility in extensions, push-down theorem on class numbers, Minkowski's constant, extensions without unramified subextensions and class number divisibility, class number divisibility in  -extensions, class number divisibility in cyclic extensions, topics on ideal class groups and discriminants
| Other names: |
ideal classes |
| Also defines: |
class number, ideal class group, class group |
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Cross-references: fractional ideals, subgroup, ideal group, quotient group, abelian group, multiplication, group, operation, semigroup, product of ideals, Abelian semigroup, equivalence classes, equivalence relation, relation, algebraic integers, ring, ideals, number field
There are 28 references to this entry.
This is version 19 of ideal class, born on 2002-04-23, modified 2008-01-23.
Object id is 2869, canonical name is IdealClass.
Accessed 7666 times total.
Classification:
| AMS MSC: | 11R29 (Number theory :: Algebraic number theory: global fields :: Class numbers, class groups, discriminants) |
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Pending Errata and Addenda
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![$ [\mathfrak{a}]$](http://images.planetmath.org:8080/cache/objects/2869/l2h/img25.png "$ [\mathfrak{a}]$"){kind=small}
![$ [\mathfrak{b}]$](http://images.planetmath.org:8080/cache/objects/2869/l2h/img26.png "$ [\mathfrak{b}]$"){kind=small}
![$\displaystyle [\mathfrak{a}] \cdot [\mathfrak{b}]=[\mathfrak{a} \mathfrak{b}] $](http://images.planetmath.org:8080/cache/objects/2869/l2h/img28.png "$\displaystyle [\mathfrak{a}] \cdot [\mathfrak{b}]=[\mathfrak{a} \mathfrak{b}] $"){kind=small}
![$ {\cal C} = \{ [\mathfrak{a}] \mid \mathfrak{a} \neq (0), \mathfrak{a}$](http://images.planetmath.org:8080/cache/objects/2869/l2h/img29.png "$ {\cal C} = \{ [\mathfrak{a}] \mid \mathfrak{a} \neq (0), \mathfrak{a}$"){kind=small}
an ideal of 
