Graded module
= Graded module
{title2=$M=\bigoplus_dM_d$}
A graded module over a <graded ring> $R=\bigoplus_iR_i$ is an $R$-<module> with a <direct sum> decomposition $M=\bigoplus_dM_d$ satisfying $R_iM_d\subseteq M_{i+d}$. A graded homomorphism preserves these degrees. Over a <polynomial ring> with positive variable degrees, a <finitely generated module> of this kind is bounded below and has finite-dimensional graded components over the coefficient <field>.