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Kaplansky zero-divisor counterexamples

Torsion gives elementary zero divisors.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

Torsion gives elementary zero divisors. Kaplansky’s conjecture instead asks whether removing torsion suffices; positive results for particular torsion-free classes do not settle that universal assertion.

The construction is in characteristic two. It does not establish a counterexample over every field, and it is distinct from the separate direct-finiteness claim.

Why it matters

If correct, refutes the stated zero-divisor conjecture while retaining torsion-freeness and finite presentation.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The construction is in characteristic two. It does not establish a counterexample over every field, and it is distinct from the separate direct-finiteness claim.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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