Definition:Subset Product/Singleton

Definition
Let $\left({S, \circ}\right)$ be an algebraic structure.

Let $A \subseteq S$ be a subset of $S$.

Then:
 * $(1): \quad a \circ S := \left \{{a}\right\} \circ S$
 * $(2): \quad S \circ a := S \circ \left \{{a}\right\}$

where $\left \{{a}\right\} \circ S$ and $S \circ \left \{{a}\right\}$ denote the subset product of $\left \{{a}\right\}$ with $S$.

That is:
 * $a \circ S = \left\{{a \circ s: s \in S}\right\}$
 * $S \circ a = \left\{{s \circ a: s \in S}\right\}$