e/Group ring

Information
has gloss	eng: 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.
lexicalization	eng: group ring
instance of	(noun) a set of points such as those of a closed surface or an analogue in three or more dimensions manifold

Meaning
Esperanto
has gloss	epo: En matematiko, la grupa algebro estas ĉiu el diversaj konstruoj por asigni al grupo (loke kompakta topologia grupo, aŭ grupo sen topologio, kio estas diskreta grupo) ringon aŭ algebron, tiel ke la grupa multipliko igas la multiplikon en la ringo aŭ algebro. Tiel ili estas similaj al la grupa ringo asociita al diskreta grupo.
lexicalization	epo: grupa algebro
French
has gloss	fra: En mathématiques, l algèbre dun groupe fini sinscrit dans le cadre de la théorie des représentations dun groupe fini.
lexicalization	fra: Algebre d'un groupe fini
lexicalization	fra: algèbre d'un groupe fini
Japanese
has gloss	jpn: 数学において、群環（ぐんかん、group ring）あるいは群多元環（ぐんたげんかん、group algebra）とは、与えられた群の元を生成元とし、適当な環を係数にもつ自由加群のことである。群環は、特に有限群の表現論において重要な役割を果たす代数的構造である。
lexicalization	jpn: 群環
Chinese
has gloss	zho: 在抽象代數中，群環是從一個群 G 及交換環 R 構造出的環，通常記為 R[G] 或 RG。其定義為：
lexicalization	zho: 群環