Description
Ideal I ⊆ R: subgroup under +, absorbs multiplication (rI ⊆ I, Ir ⊆ I). Quotient ring R/I. Ring homomorphism, kernel, image. First, second, third isomorphism theorems.
Dependency Flowchart
Note: Arrows mean "depends on". Assumes Chart 1.
graph TD
D1["Def: Ideal\nI subgroup, rI Ir ⊆ I"]
D2["Def: Quotient R/I\ncosets, ring structure"]
D3["Def: Ring homomorphism\nφ preserves + · 1"]
D4["Def: Kernel\nker φ = φ⁻¹0"]
T1["Thm: FIT\nR/ker φ ≅ im φ"]
T2["Thm: 2nd iso\n(I+J)/J ≅ I/(I∩J)"]
T3["Thm: 3rd iso\n(R/I)/(J/I) ≅ R/J"]
D1 --> D2
D3 --> D4
D2 --> T1
D4 --> T1
D1 --> T2
D2 --> T3
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class D1,D2,D3,D4 definition
class T1,T2,T3 theorem
Color Scheme
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Process Statistics
- Nodes: 7
- Edges: 8
- Definitions: 4
- Theorems: 3