Cohomologie Locale Des Faisceaux Coherents (Sga 2): Seminaire De Geometrie Algebrique Du Bois Marie 1962 (Documents Mathematiques)
《Cohomologie Locale Des Faisceaux Coherents (Sga 2): Seminaire De Geometrie Algebrique Du Bois Marie 1962 (Documents Mathematiques)》 · 第 4 页 · Chapter 1，Section 1.1「Definitions and Examples」
Another way to define a representation of a group is in terms of the group algebra. We define the group algebra $RG$ (or $R[G]$) of $G$ over $R$ to be the free $R$-module with the elements of $G$ as an $R$-basis and with multiplication given on the basis elements by group multiplication. The elements of $RG$ are the (formal) $R$-linear combinations of group elements, and the multiplication of the basis elements is extended to arbitrary elements using bilinearity of the operation.