Source labels openarXiv · Commutative algebra
Zariski Cancellation
The Zariski Cancellation Problem: every polynomial ring over a field k of characteristic
0 is cancellative.
Source checked Jul 26, 20261 pinned Lean statementInspect problem
Questions, not proof records
Open-problem statements, with their sources attached.
Each statement record keeps the mathematical question, a dated status source, accessible references, and any pinned Lean formulation separate from proof verification.
“Open” is a dated source assertion. In these pinned sources,
sorry marks an admitted statement, not a proof. Source indexing does not mean the formulation has been independently built or certified by Therefore.Source labels openMathOverflow · Commutative algebra
Mathoverflow 507128
There exists a proper ideal I in a (commutative) total ring R of fractions that is an
invertible module. If I ⊊ R is such an example, I must have infinite order in the Picard group,
and R must not be Noetherian (otherwise it must be semi-local and therefore have trivial Picard
group).
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Source labels openWikipedia · Commutative algebra
Pierce–Birkhoff conjecture
The Pierce-Birkhoff conjecture states that for every real piecewise-polynomial function
f : ℝⁿ → ℝ, there exists a finite set of polynomials gᵢⱼ ∈ ℝ[x₁, ..., xₙ] such that
f = supᵢ infⱼ(gᵢⱼ).
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Source labels openMathOverflow · Number theory
17560
If and are integers, then must be an integer.
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