Definition:Support of Element of Direct Product

Definition
Let $(S_i,\circ_i)_{i\in I}$ be a family of algebraic structures.

Let $S=\displaystyle\prod_{i\in I}S_i$ be their direct product.

Let $e_i$ be an identity of $S_i$ for all $i\in I$.

Let $m=(m_i)_{i\in I}\in S$.

The support of $m$ is $\left\{i\in I:m_i\neq e_i\right\}$.