The Skolem-Noether Theorem states that any two algebra embeddings of a simple algebra into a finite-dimensional central simple algebra over the same field are related by an inner automorphism of the larger algebra, meaning conjugation by some invertible element carries one embedding onto the other. Named for Thoralf Skolem and Emmy Noether, it is a foundational uniqueness result for central simple algebras, showing their internal symmetries are as rigid as possible.
Facts
StatementGiven k-algebra homomorphisms f, g : A to B, there exists a unit b in B such that for all a in A: g(a) = b times f(a) times b to the power of negative 1. 1 Classification
Statement Form Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Skolem-Noether theorem, Wikipedia
Proved By
Sources
1. Skolem-Noether theorem, Wikipedia
Statement section
Given k-algebra homomorphisms f, g : A to B, there exists a unit b in B such that for all a in A: g(a) = b times f(a) times b to the power of negative 1.
History section
The theorem was first published by Thoralf Skolem in 1927 in his paper Zur Theorie der assoziativen Zahlensysteme
- In Branch: Ring Theory, Lead sentence
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