Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The degree of a finite field extension
Definition
Let be a field extension. Scalar multiplication by , together with addition in , makes an -vector space. The extension is finite when this vector space is finite-dimensional. In that case its degree is
No numerical degree is assigned here to an infinite-dimensional extension.
Depends on
Used by
- Every finite extension of a finite field is simple Corollary
- A finite extension has degree one if and only if the two fields are equal Proposition
- For finite subextensions in a common field, [EE':F]≤ [E:F][E':F] Proposition
- Every finite field extension is algebraic Theorem
- Every finite field has order pⁿ for a unique prime characteristic p and positive integer n Theorem
- Tower law for finite extensions: [L:F]=[L:K][K:F] Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 55 results over 19 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- A. W. Knapp, Basic Algebra, 2nd ed., Chapter IX, Section 1 (standard reference, not scraped)