| dbo:abstract |
En algèbre générale, il est possible de combiner plusieurs anneaux pour former un anneau appelé anneau produit. (fr) In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the category of rings. Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings. For example, the Chinese remainder theorem may be stated as: if m and n are coprime integers, the quotient ring is the product of and (en) 数学において、いくつかの環を1つの大きい直積環、積環 (product ring) に合併することができる。これは次のようにされる： I がある添え字集合で Ri が I のすべての i に対して環であれば、カルテジアン積 Πi ∈ I Ri は演算を 成分ごとの演算として定義することによって環にできる。 得られる環は環 Ri の直積 (direct product) と呼ばれる。有限個の環の直積は環の直和 (direct sum) と一致する。 (ja) In de ringtheorie, een deelgebied van de wiskunde, is het mogelijk om verschillende ringen te combineren tot een grotere productring. Het directe product van de samenstellende ringen. Het directe product van de ringen , met een willekeurige indexverzameling wordt gevormd door het cartesisch product met als bewerkingen de coördinaatsgewijze uitgevoerde bewerkingen van de samenstellende ringen. Dat houdt in dat voor de elementen en geldt: en (nl) |
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En algèbre générale, il est possible de combiner plusieurs anneaux pour former un anneau appelé anneau produit. (fr) In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the category of rings. Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings. For example, the Chinese remainder theorem may be stated as: if m and n are coprime integers, the quotient ring is the product of and (en) 数学において、いくつかの環を1つの大きい直積環、積環 (product ring) に合併することができる。これは次のようにされる： I がある添え字集合で Ri が I のすべての i に対して環であれば、カルテジアン積 Πi ∈ I Ri は演算を 成分ごとの演算として定義することによって環にできる。 得られる環は環 Ri の直積 (direct product) と呼ばれる。有限個の環の直積は環の直和 (direct sum) と一致する。 (ja) In de ringtheorie, een deelgebied van de wiskunde, is het mogelijk om verschillende ringen te combineren tot een grotere productring. Het directe product van de samenstellende ringen. Het directe product van de ringen , met een willekeurige indexverzameling wordt gevormd door het cartesisch product met als bewerkingen de coördinaatsgewijze uitgevoerde bewerkingen van de samenstellende ringen. Dat houdt in dat voor de elementen en geldt: en (nl) |
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Produit d'anneaux (fr) 環の直積 (ja) Product van ringen (nl) Product of rings (en) |
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