Homogeneous element

Definition
A homogeneous element in a graded ring is an element that lies in one of the graded components (also called homogeneous component).

For any nonzero homogeneous element, its degree is the $$d$$ for which it lies in the $$d^{th}$$ graded component.

Note that $$0$$ is considered a homogeneous element, since it lies in every graded component.