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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.".
- Group_ring wikiPageID "349223".
- Group_ring wikiPageRevisionID "604471248".
- Group_ring author "A. A. Bovdi".
- Group_ring hasPhotoCollection Group_ring.
- Group_ring id "G/g045220".
- Group_ring title "Group algebra".
- Group_ring subject Category:Harmonic_analysis.
- Group_ring subject Category:Representation_theory_of_groups.
- Group_ring subject Category:Ring_theory.
- Group_ring comment "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.".
- Group_ring label "Algèbre d'un groupe fini".
- Group_ring label "Group ring".
- Group_ring label "Gruppen-C*-Algebra".
- Group_ring label "Групповое кольцо".
- Group_ring label "群環".
- Group_ring label "群環".
- Group_ring sameAs Gruppen-C*-Algebra.
- Group_ring sameAs Algèbre_d'un_groupe_fini.
- Group_ring sameAs 群環.
- Group_ring sameAs 군환.
- Group_ring sameAs m.01z1qd.
- Group_ring sameAs Q2602722.
- Group_ring sameAs Q2602722.
- Group_ring wasDerivedFrom Group_ring?oldid=604471248.
- Group_ring isPrimaryTopicOf Group_ring.