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Source labels openChecked July 26, 2026

WikipediaAssociative algebras

Köthe conjecture: Matrix Over Kother Radical

The Köthe conjecture: for any positive integer n, the Köthe radical of R is the matrix ideal M_2(Nil*(R)).

Mathematical statement

The Köthe conjecture: for any positive integer n, the Köthe radical of R is the matrix ideal M_2(Nil*(R)).

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

KotherConjecture.variants.matrixOver_KotherRadical

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem KotherConjecture.variants.matrixOver_KotherRadical    {I : TwoSidedIdeal R} (hI : IsNil I) (n : Type*) [Fintype n] :    matrix n (Nil* R) = Nil* (Matrix n n R) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References