Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
gptkb:Ring_theory
|
| gptkbp:defines |
An ideal I of a ring R such that if some power of an element r is in I, then r is in I
|
| gptkbp:field |
gptkb:Algebraic_geometry
gptkb:Commutative_algebra |
| https://www.w3.org/2000/01/rdf-schema#label |
Radical ideal
|
| gptkbp:introduced |
gptkb:Emmy_Noether
|
| gptkbp:notation |
√I
|
| gptkbp:property |
Every prime ideal is a radical ideal
Every radical ideal is equal to its own radical If I is a radical ideal, then R/I is reduced Intersection of prime ideals is a radical ideal The radical of an ideal is a radical ideal Sum and intersection of radical ideals are radical ideals |
| gptkbp:relatedTo |
gptkb:Prime_ideal
Nilradical Radical of an ideal |
| gptkbp:usedIn |
gptkb:Hilbert's_Nullstellensatz
Algebraic set Variety (algebraic geometry) |
| gptkbp:bfsParent |
gptkb:Prime_ideal
|
| gptkbp:bfsLayer |
7
|