「group ring」を英語から日本語に翻訳する

(algebra) 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 . [..]