A ring of polynomials is a mathematical structure formed by polynomials with coefficients from a specific ring, such as the integers or real numbers. In this context, polynomials are expressions that involve variables raised to non-negative integer powers, combined using addition and multiplication. The set of all such polynomials can be denoted as R[x], where R represents the coefficient ring and x is the variable. In a ring of polynomials, you can perform operations like addition, subtraction, and multiplication, and the results will also be polynomials. This structure follows certain properties, such as associativity and distributivity, making it a fundamental concept in algebra. Rings of polynomials are essential in various fields, including algebraic geometry and computer algebra.