\begin{definition}[Definition:Extension of Operation]
Let $\left({S, \circ}\right)$ be a magma.
Let $\left({T, \circ \restriction_T}\right)$ be a submagma of $\left({S, \circ}\right)$, where $\circ \restriction_T$ denotes the restriction of $\circ$ to $T$.
Then:
: '''$\left({S, \circ}\right)$ is an extension of $\left({T, \circ \restriction_T}\right)$'''
or
: '''$\left({S, \circ}\right)$ extends $\left({T, \circ \restriction_T}\right)$'''
We can use the term directly to the operation itself and say:
: '''$\circ$ is an extension of $\circ \restriction_T$'''
or:
: '''$\circ$ extends $\circ \restriction_T$'''
\end{definition}