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- Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is the set of elements of the given group.en.wikipedia.org/wiki/Group_ringThe group ring k[G] is defined to be the set of all finite k linear combinations of elements of G: a for all G and a = 0 for almost all. For example, R[Z/3] is the set of all linear combinations where + y + z 2 where x, y, z R. I.e., R[Z/3] = R3. In general k[G] is a vector space over k with G as a basis.people.brandeis.edu/~igusa/Math101bS07/Math101…
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