Description
Field: commutative ring with unity where every nonzero element is a unit. Extension K/F: F subfield of K. Degree [K:F]. Finite extension, algebraic extension, transcendental element.
Dependency Flowchart
Note: Arrows mean "depends on".
graph TD
D1["Def: Field\ncomm ring, K* group"]
D2["Def: Extension K/F\nF subfield of K"]
D3["Def: Degree [K:F]\ndim_F K"]
D4["Def: Algebraic α\nroot of poly over F"]
D5["Def: Transcendental\nnot algebraic"]
T1["Thm: Tower law\n[K:F]=[K:E][E:F]"]
T2["Thm: F(α) ≅ F[x]/m_α\nm_α min poly"]
D1 --> D2
D2 --> D3
D2 --> D4
D4 --> D5
D3 --> T1
D4 --> T2
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class D1,D2,D3,D4,D5 definition
class T1,T2 theorem
Color Scheme
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Process Statistics
- Nodes: 7
- Edges: 7
- Definitions: 5
- Theorems: 2