Correct Terminology in the Context of Rings

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Suppose I have a ring $(A, ◦, •)$ where $A$ is a set of elements $\{α, β, γ,\ldots\}$.

Can $◦$ and $•$ with which the ring is equipped be properly termed, in English, its "internal laws of composition," or is "internal binary operators" better in this context?

Are $A$, $◦$, and $•$ taken together—when written as $(A, ◦, •)$, e.g.—properly termed a ternary, triad, or triplet, in English?

I am trying to translate the Spanish:

Se denomina anillo a una terna $(A, ◦, •)$, donde $A$ es un conjunto de elementos $\{α, β, γ, …\}$, dotado de dos leyes de composición internas, $◦$ y $•$, …

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I would translate it as:

"A ring is a triplet $(A, \circ, \bullet)$, where $A$ is the set $\{\alpha, \beta, \gamma, \ldots, \}$ with two binary operations $\circ$ and $\bullet$".

This is not a literal translation, but the literal translation would be a bit awkward in my opinion.

As is clear now, I choose to translate 'internal laws of composition' as 'binary operations'.

'Internal binary operations' is uncommon and redundant since the definition of binary operation entails that it is 'internal'.