In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian product Πi in I Ri can be turned into a ring by defining the operations coordinatewise, i.e. (ai) + (bi) = (ai + bi) (ai) · (bi) = (ai · bi) The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings R1,... ,Rk is also written as R1 × R2 × ...
| Property | Value |
|---|
| dbpprop:abstract
|
- In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian product Πi in I Ri can be turned into a ring by defining the operations coordinatewise, i.e. (ai) + (bi) = (ai + bi) (ai) · (bi) = (ai · bi) The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings R1,... ,Rk is also written as R1 × R2 × ... × Rk.
- En algèbre générale, il est possible de combiner plusieurs anneaux pour former un anneau appelé anneau produit.
|
| dbpprop:hasPhotoCollection
| |
| rdf:type
| |
| rdfs:comment
|
- In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian product Πi in I Ri can be turned into a ring by defining the operations coordinatewise, i.e. (ai) + (bi) = (ai + bi) (ai) · (bi) = (ai · bi) The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings R1,... ,Rk is also written as R1 × R2 × ...
- En algèbre générale, il est possible de combiner plusieurs anneaux pour former un anneau appelé anneau produit.
|
| rdfs:label
|
- Product of rings
- Produit d'anneaux
|
| owl:sameAs
| |
| skos:subject
| |
| foaf:page
| |
| is dbpprop:redirect
of | |
| is owl:sameAs
of | |
![[RDF Data]](/statics/sw-cube.png)
