A polynomial admitting a multiplicative inverse. In the polynomial ring R[x], where R is an integral domain, the invertible polynomials are precisely the constant polynomials a such that a is an invertible element of R. In particular, if R is a field, the invertible polynomials are all constant polynomials except the zero polynomial. If R is not an integral domain, there may be in R[x] invertible polynomials that are not constant. In Z_4[x], for instance, we have: (2^_ x + 1^_)(2^_ x + 1^_) = 1^_, which shows that the polynomial 2^_ x + 1^_ is invertible, and inverse to itself.

invertible | invertible element | invertible polynomial map