Definition:Extension of Operation
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This page is about extensions of operations. For other uses, see Extension.
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 $\circ \restriction_T$