All open problems
Source labels openChecked July 26, 2026
Kaplansky's Conjectures
The idempotent conjecture*
Mathematical statement
The idempotent conjecture*
If G is torsion-free, then K[G] has no non-trivial idempotents.
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
idempotent_conjecture
Complete statement target, proof intentionally absentLean 4
theorem idempotent_conjecture (a : MonoidAlgebra K G) (h : IsIdempotentElem a) : a = 0 ∨ a = 1 := 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