Questions, not proof records
Each statement record keeps the mathematical question, a dated status source, accessible references, and any pinned Lean formulation separate from proof verification.
sorry marks an admitted statement, not a proof. Source indexing does not mean the formulation has been independently built or certified by Therefore.The zero-divisor conjecture*
If G is torsion-free, then the group algebra K[G] has no non-trivial zero divisors.
The idempotent conjecture*
If G is torsion-free, then K[G] has no non-trivial idempotents.
The Köthe conjecture: In any ring, the sum of two nil left ideals is nil.
The Köthe conjecture: every left nil radical is contained in the Köthe radical.
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).
The Köthe conjecture: for any nil ideal I of R, the matrix ideal M_2(I) is a nil ideal
of the matrix ring M_2(R).
The Köthe conjecture: for any positive integer n, the Köthe radical of R is the matrix ideal M_2(Nil*(R)).