 Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series, matrices and functions.A ring is an abelian group with a second binary operation that is associative, is distributive over the abelian group operation, and has an identity element (this last property is not required by some authors, see ).By extension from the integers, the abelian group operation is called "addition" and the second binary operation is called "multiplication".