Matches in DBpedia 2016-04 for { ?s ?p "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 one-to-one with the given group. As a ring, its addition law is that of the free module and its multiplication extends \"by linearity\" the given group law on the basis. Less formally, a group ring is a generalization of a given group, by attaching to each element of the group a \"weighting factor\" from a given ring.If the given ring is commutative, a group ring is also referred to as a group algebra, for it is indeed an algebra over the given ring.The apparatus of group rings is especially useful in the theory of group representations."@en }
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- Group_ring abstract "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 one-to-one with the given group. As a ring, its addition law is that of the free module and its multiplication extends \"by linearity\" the given group law on the basis. Less formally, a group ring is a generalization of a given group, by attaching to each element of the group a \"weighting factor\" from a given ring.If the given ring is commutative, a group ring is also referred to as a group algebra, for it is indeed an algebra over the given ring.The apparatus of group rings is especially useful in the theory of group representations.".