The stable coordinate conjecture asserts over a field 
of characteristic zero that a polynomial
![f in k[x_1,...,x_n]](/images/equations/StableCoordinateConjecture/Inline2.svg)
which becomes a coordinate polynomial after
adjoining finitely many independent variables is already a coordinate
polynomial in the original ring. The one-added-variable formulation implies the
finite-variable formulation by successive applications.
Stable Coordinate Conjecture
See also
Abhyankar-Sathaye Conjecture, Coordinate Polynomial, Polynomial Ring, Zariski Cancellation ProblemExplore with Wolfram|Alpha
References
Makar-Limanov, L.; van Rossum, P.; Shpilrain, V.; and Yu, J.-T. "The Stable Equivalence and Cancellation Problems." Comment. Math. Helv. 79, 341-349, 2004. https://doi.org/10.1007/s00014-003-0796-3.Cite this as:
Weisstein, Eric W. "Stable Coordinate Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StableCoordinateConjecture.html