 Polynomial ring

The polynomial ring $R[X]$ consists of polynomials in an indeterminate $X$ with coefficients in a ring $R$.

A **polynomial ring** is a mathematical structure formed from polynomials over a given coefficient ring or field. Formally, if \( R \) is a ring (or a field), then the polynomial ring \( R[x] \) consists of all polynomials in the variable \( x \) with coefficients in \( R \).

The polynomials together with polynomial addition and multiplication form a commutative ring.