Definition:Extension of Operation

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Definition

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 $\circ \restriction_T$


Also see