Is there any study of Mathematical systems that has the same n-binary operations?

Question

I am currently studying Groups and Rings. Groups and Rings are types of Mathematical System. Now, imagine an ordered (n+1)-tuple (X, *₁,*₂,...,*ₙ) where X is a non-empty set and *ᵢ is a binary operation on X, i = 1,2,3, ... ,n. My question is that is there a term for a Mathematical system where all the binary operations are the same?

Answer 1

Considering a structure $\langle X, *_1, \dots, *_n \rangle$ where $*_1 = \dots = *_n$ and $n >0$, is equivalent to considering the structure $\langle X, *_1 \rangle$. So in most cases there is little need to give a special term to this situation.