Abstract by Thomas Draper
Nilpotent Polynomials and Nilpotent Coefficients
A ring element is nilpotent if when raised to some positive integer power it becomes zero. A general problem is determining what conditions are required on a coefficient ring for every nilpotent polynomial to have nilpotent coefficients. We constructed an example of a ring where the product of any two nilpotent elements is zero, and yet there exists a polynomial over that ring, with non-nilpotent coefficients, of degree seven whose square is zero. This shows that even under these rather strong conditions there is a counterexample. The degree in this example is minimal.