group ring

For any group G, the group ring [G] is defined to be the ring whose additive groupMathworldPlanetmath is the abelian groupMathworldPlanetmath of formal integer linear combinationsMathworldPlanetmath of elements of G, and whose multiplication operation is defined by multiplication in G, extended –linearly to [G].

More generally, for any ring R, the group ring of G over R is the ring R[G] whose additive group is the abelian group of formal R–linear combinations of elements of G, i.e.:


and whose multiplication operation is defined by R–linearly extending the group multiplication operation of G. In the case where K is a field, the group ring K[G] is usually called a group algebra.

Title group ring
Canonical name GroupRing
Date of creation 2013-03-22 12:13:27
Last modified on 2013-03-22 12:13:27
Owner djao (24)
Last modified by djao (24)
Numerical id 8
Author djao (24)
Entry type Definition
Classification msc 20C05
Classification msc 20C07
Classification msc 16S34
Defines group algebra