In mathematics, the study of the structure of a set of objects (e.g., numbers) with two combining operations (e.g., addition and multiplication).
Such a system, known as a field, must satisfy certain properties: associative law , commutative law , distributive law , an additive identity ("zero"), a muliplicative identity ("one"), additive inverses (see inverse function ), and multiplicative inverses for nonzero elements. The sets of rational number s, real number s, and complex number s are fields under ordinary addition and multiplication. The investigation of polynomial equations and their solutions led to the development of field theory.