This question describes a combinatorial game based on commutative algebra where the game state is a ring and a move is taking the quotient by a nonzero element:

> [A Game on Noetherian Rings][1]

The hard problem is to either determine which positions are winning and which are losing, or to show that the previous problem has no solution.



  [1]: https://mathoverflow.net/questions/93276/a-game-on-noetherian-rings