For any group , the group ring is defined to be the ring whose additive group is the abelian group of formal integer linear combinations of elements of , and whose multiplication operation is defined by multiplication in , extended –linearly to .
More generally, for any ring , the group ring of over is the ring whose additive group is the abelian group of formal –linear combinations of elements of , i.e.:
and whose multiplication operation is defined by –linearly extending the group multiplication operation of . In the case where is a field, the group ring is usually called a group algebra.
|Date of creation||2013-03-22 12:13:27|
|Last modified on||2013-03-22 12:13:27|
|Last modified by||djao (24)|