I am trying to understand Definition 3.1 of the following paper. We have a unital ring $R$ with a $\mathbb{Z}$-grading $(R_i)$ that is commutative i.e. $xy=(-1)^{|x||y|}yx$, and an $R$-module $I$ with a $\mathbb{Z}$-grading $(M_i)$ i.e. $R_iM_j\subseteq M_{i+j}$. $J$ is a graded ideal which (as far as I can tell) means that $J_i=J\cap R_i$ for all $i$. Let $d\in\mathbb{Z}$.
I am trying to understand the role of $\Sigma$ in $\Sigma^d J$. I'm sure it means some kind of shift (changing degree by $d$) but am unsure how this is defined explicitly, and how it necessarily leads to a well-defined grading. How should I make sense of this?