Element Functions
Why
Take an element of an algebra, and consider the function defined on the ground set which maps elements to the result of the operation applied to the fixed element and the given element.
Definition
Let $(A, +)$ be an algebra.
For each $a \in A$, denote by $+_a: A \to A$
the function defined by
\[
+_a(b) = a + b.
\]
Similarly, denote by $+^a: A \to A$ the
function defined by
\[
+^{a}(b) = b + a.
\]
The idea is that elements of an algebra can always be associated with functions.