Shifted graded module

Let $𝔄 \leq 𝔅$ be a submonoid. Let $𝑅$ be a $𝔄$ -graded ring and $𝑀$ be $𝔄$ -graded module over $𝑅$ . Given some $𝛽 \in 𝔅$ , we can define a $𝛽$ -shifted gradation on $𝑀$ with the following relabelling

𝑉 𝛼 \mapsto 𝑉 𝛼 + 𝛽

where we consider $𝐴 𝛾 = 0$ for $𝛾 \notin 𝔄$ and $𝑉 𝛾 = 0$ for $𝛾 \notin 𝔄 + 𝛽$ . #m/thm/module

#state/tidy | #lang/en | #SemBr