Homogeneous ideal

An ideal $\mathfrak{a}$ of a graded ring $S={\oplus }_p{S}_d$ is called homogeneous if it satisfies the condition:
If $a\in \mathfrak{a}$ and $a=\sum _d{a}_d$ with $a_d\in S_d$, then each $a_d\in \mathfrak{a}$.