Is there a specific name for a set with a defined binary operation, that is not a group?

Question

Is there a specific name for a set with a defined binary operation, that is not a group? e.g.:

({1, 2, 3, 6}, +).

Answer 1

A binary operation is a map $\circ : A \times A \to A$, which you don't actually have since $1 + 3$ is outside your set.

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However, the term for a set equipped with a binary operation is a magma.