Graded vector space conditions Wikipedia define the graded ( ring, module, vector space, ...) as here
I noted that in the rings and modules it required the condition of inclusion but in the vector spaces it did not. just the direct sum condition ..why ??
Any hint ? 

Any inclusion V -> W of vector spaces creates a direct sum decomposition $W \cong V \oplus V^{\perp}$.
A graded vector space $W = V_1 \oplus V_2$ would have graded part ($\le 2$) equal to W not $V_2$.
