Definition:Subset Product/Singleton

Definition

Let $\struct {S, \circ}$ be an algebraic structure.

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

Then:

$(1): \quad a \circ S := \set a \circ S$
$(2): \quad S \circ a := S \circ \set a$

where $\set a \circ S$ and $S \circ \set a$ denote the subset product of $\set a$ with $S$.

That is:

$a \circ S = \set {a \circ s: s \in S}$
$S \circ a = \set {s \circ a: s \in S}$