Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A subset I of a ring R that is an additive subgroup and absorbs multiplication by elements of R
|
| gptkbp:example |
the set of even integers in the ring of integers
the set of polynomials divisible by x in the ring of polynomials |
| gptkbp:field |
ring theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ideal I
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:namedFor |
gptkb:Richard_Dedekind
|
| gptkbp:property |
If a, b ∈ I, then a + b ∈ I
If r ∈ R and a ∈ I, then r·a ∈ I and a·r ∈ I (for two-sided ideals) |
| gptkbp:relatedTo |
ideal (ring theory)
|
| gptkbp:type |
two-sided ideal
left ideal right ideal |
| gptkbp:usedIn |
homomorphism theorems
quotient ring construction |
| gptkbp:bfsParent |
gptkb:Local_cohomology
|
| gptkbp:bfsLayer |
7
|