group ring

Noun

 * 1)  Given ring R with identity not equal to zero, and group $$G = \{g_1, g_2, ..., g_n\}$$, the group ring RG has elements of the form $$ a_1 g_1 + a_2 g_2 + ... + a_n g_n $$ (where $$a_i \isin R $$) such that the sum of $$ a_1 g_1 + a_2 g_2 + ... + a_n g_n $$ and $$ b_1 g_1 + b_2 g_2 + ... + b_n g_n $$ is $$ (a_1 + b_1) g_1 + (a_2 + b_2) g_2 + ... + (a_n + b_n) g_n$$ and the product is $$ \sum_{k=1}^n \left ( \sum_{g_i g_j = g_k} a_i b_j \right ) g_k $$.

Translations

 * Portuguese: anel de grupo