group ring en · NOUN
Meanings
- 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_1g_1+a_2g_2+...+a_ng_n (where a_i isin R) such that the sum of a_1g_1+a_2g_2+...+a_ng_n and b_1g_1+b_2g_2+...+b_ng_n is (a_1+b_1)g_1+(a_2+b_2)g_2+...+(a_n+b_n)g_n and the product is ∑ₖ₌₁ⁿ(∑_(g_ig_j=g_k)a_ib_j)g_k.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| group rings | Number=Plur | lexicographic |
Hypernyms
algebra over a ring · ring · free module
Synonyms
Translations (2)
pt anel de grupo (Translations) · pl pierścień grupowy (Translations)