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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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    @J.D.: I don't like that: "endomap" suggests a map form a set to *itself*.2012-03-25

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

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    @BillDubuque I $f$ind it strange too, but it makes sense. At least, it does not makes any _other_ sense. Shall we conclude there is no unanimous terminology? There is [in French](http://$f$r.wikipedia.org/wiki/Loi_de_composi$t$ion_interne) and [German](http://de.wikipedia.org/wiki/Zweistellige_Verkn%C3%BCpfung): internal.2012-03-25