group ring

名词noun

1. 1(algebra) Given ring R with identity not equal to zero, and group G={g1,g2,...,gn}, the group ring RG has elements of the form a1g1+a2g2+...+angn (where ai∈R) such that the sum of a1g1+a2g2+...+angn and b1g1+b2g2+...+bngn is (a1+b1)g1+(a2+b2)g2+...+(an+bn)gn and the product is ∑k=1n(∑gigj=gkaibj)gk.