Primary ideal, associated primes. Lasker–Noether: I=∩Qᵢ. Uniqueness of isolated components.
graph TD
D1["Def: Primary ideal\nxy∈Q⇒x∈Q or yⁿ∈Q"]
D2["Def: Associated prime\nP=√(0:M)"]
D3["Def: Isolated comp\nminimal ass"]
D4["Def: Radical\n√I = {x: xⁿ∈I}"]
T1["Thm: Lasker–Noether\nI=Q₁∩...∩Qₙ"]
T2["Thm: Ass(M) finite"]
T3["Thm: Uniqueness\nisolated comp unique"]
T4["Thm: √primary = prime"]
T5["Thm: First uniqueness\nradicals"]
D1 --> T1
D2 --> T2
D3 --> T3
D4 --> T4
T1 --> T3
T1 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
Frontier: math.AC