Given a field$K$ and a polynomial$p \in K[x]$, a polynomial modulo $p$ is an element of the quotient ring$q \in K[x]/p K[x]$. The quotient ring itself is called the ring of polynomials modulo $p$.

Examples

The Gaussian rationals are the rational polynomials $\mathbb{Q}[x]$ modulo $x^2 + 1$.

The complex numbers are the real polynomials $\mathbb{R}[x]$ modulo $x^2 + 1$.

The dual numbers are the real polynomials $\mathbb{R}[x]$ modulo $x^2$.