|
|
|
|
"group ring" is owned by djao.
|
|
(view preamble)
| Also defines: |
group algebra |
|
|
Cross-references: field, combinations, operation, multiplication, linear combinations, integer, abelian group, additive group, ring, group
There are 13 references to this entry.
This is version 4 of group ring, born on 2002-01-23, modified 2002-11-06.
Object id is 1595, canonical name is GroupRing.
Accessed 7128 times total.
Classification:
| AMS MSC: | 20C05 (Group theory and generalizations :: Representation theory of groups :: Group rings of finite groups and their modules) | | | 20C07 (Group theory and generalizations :: Representation theory of groups :: Group rings of infinite groups and their modules) | | | 16S34 (Associative rings and algebras :: Rings and algebras arising under various constructions :: Group rings , Laurent polynomial rings) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
![$ \mathbb{Z}[G]$](http://images.planetmath.org:8080/cache/objects/1595/l2h/img2.png "$ \mathbb{Z}[G]$"){kind=small}
![$ \mathbb{Z}[G]$](http://images.planetmath.org:8080/cache/objects/1595/l2h/img6.png "$ \mathbb{Z}[G]$"){kind=small}
![$ R[G]$](http://images.planetmath.org:8080/cache/objects/1595/l2h/img10.png "$ R[G]$"){kind=small}
![$\displaystyle R[G] := \left\{\left. \sum_{i=1}^n r_i g_i\ \right\vert\ r_i \in R,\ g_i \in G\right\}, $](http://images.planetmath.org:8080/cache/objects/1595/l2h/img13.png "$\displaystyle R[G] := \left\{\left. \sum_{i=1}^n r_i g_i\ \right\vert\ r_i \in R,\ g_i \in G\right\}, $")
![$ K[G]$](http://images.planetmath.org:8080/cache/objects/1595/l2h/img17.png "$ K[G]$"){kind=small}