Invertible Polynomial

A polynomial admitting a multiplicative inverse. In the polynomial ring , where is an integral domain, the invertible polynomials are precisely the constant polynomials such that is an invertible element of . In particular, if is a field, the invertible polynomials are all constant polynomials except the zero polynomial.

If is not an integral domain, there may be in invertible polynomials that are not constant. In , for instance, we have:

which shows that the polynomial is invertible, and inverse to itself.