Description
Algebraically closed field: every nonconstant polynomial has a root. Splitting field of f over F: minimal extension where f splits. Uniqueness up to F-isomorphism.
Dependency Flowchart
Note: Arrows mean "depends on". Assumes Chart 1.
graph TD
D1["Def: Algebraically closed\nevery poly has root"]
D2["Def: Splitting field\nminimal K where f splits"]
D3["Def: Algebraic closure\nF-bar of F"]
T1["Thm: Splitting field exists\nfor any f"]
T2["Thm: Splitting field unique\nup to F-iso"]
T3["Thm: Closure exists\nSteinitz"]
D1 --> D3
D2 --> T1
D2 --> T2
D1 --> T3
T1 --> T2
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class D1,D2,D3 definition
class T1,T2,T3 theorem
Color Scheme
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Process Statistics
- Nodes: 6
- Edges: 5
- Definitions: 3
- Theorems: 3