Math vocab: operator on $S$ and into $S =$?

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Is there a special name for a binary operation on the set $S$ that is also into $S$, that is unambiguous with other uses. I.e. if it's "operator on $S$", I've heard that in other places meaning the operator could map to another set $T$. I'm working on a math library in the D language.

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Are you looking for the term closed binary operation? (other reference)