Köthe conjecture: General Matrix
The Köthe conjecture: for any nil ideal I of R, the matrix ideal M_n(I) is a nil ideal of the matrix ring M_n(R).
Mathematical statement
The Köthe conjecture: for any nil ideal I of R, the matrix ideal M_n(I) is a nil ideal
of the matrix ring M_n(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.general_matrix
theorem KotherConjecture.variants.general_matrix {I : TwoSidedIdeal R} (hI : IsNil I) (n : Type*) [Fintype n] : IsNil (matrix n I) := 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