BYU

Abstract by Thomas Draper

Personal Infomation


Presenter's Name

Thomas Draper

Degree Level

Undergraduate

Co-Authors

Janez Šter
Pace Nielsen

Abstract Infomation


Department

Mathematics

Faculty Advisor

Pace Nielsen

Title

Nilpotent Polynomials and Nilpotent Coefficients

Abstract

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.