Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
gptkb:Lasker–Noether_theorem
|
| gptkbp:definedIn |
gptkb:Commutative_ring
|
| gptkbp:defines |
An ideal Q of a commutative ring R such that if ab ∈ Q and a ∉ Q, then b^n ∈ Q for some n > 0.
|
| gptkbp:field |
gptkb:Commutative_algebra
gptkb:Ring_theory |
| gptkbp:generalizes |
gptkb:Prime_ideal
|
| https://www.w3.org/2000/01/rdf-schema#label |
Primary ideal
|
| gptkbp:introduced |
gptkb:Emmy_Noether
|
| gptkbp:notation |
Q (often used for primary ideals)
|
| gptkbp:property |
If Q is a primary ideal, then R/Q has no zero divisors except nilpotent elements
If Q is a primary ideal, then every zero divisor in R/Q is nilpotent Every prime ideal is a primary ideal The radical of a primary ideal is a prime ideal |
| gptkbp:relatedTo |
gptkb:Prime_ideal
|
| gptkbp:usedIn |
Primary decomposition
|
| gptkbp:bfsParent |
gptkb:Prime_ideal
|
| gptkbp:bfsLayer |
7
|