The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, hence of all elements of the form a_1 g_1 + a_2 g_2 + ... + a_n g_n, where a_i element K and g_i element G for all i = 1, ..., n. This element can be denoted in general by sum_(g element G) a_g g, where it is assumed that a_g = 0 for all but finitely many elements of g.

algebra | group | semigroup algebra