Ideal of a cring

Definition
A subset $$I$$ of a cring $$C$$ is termed an ideal or two-sided ideal of $$C$$ if it satisfies the following conditions:


 * 1) $$I$$ is an additive subgroup of $$C$$.
 * 2) For every $$x \in I$$ and $$y \in C$$, we have $$x * y \in I$$ and $$y * x \in I$$.