Is abstract algebra (mostly?) restricted to $2$-ary operators? This may be due to my own pure ignorance but it's my experience that all abstract algebra I've been introduced to, both in actual courses and in self-studies only exclusively deals with algebraic objects consisting of a set together with one or more binary operators defined on that set, perhaps over some other algebraic structure. Not counting categories here, just "low-level"-ish stuff.
I'm an undergraduate so my knowledge is of course very limited but I can't help to wonder why I never stumble upon algebraic structures with $n$-ary operators? Is there a good reason for this, something along the lines of $n$-ary operators behave "badly" when $n>2$ or is it just my ignorance because I'm a beginner in the field?

In logic the operators are 2-ary because any function $\mathbb Z_2^n\rightarrow \mathbb Z_2$ can be expressed by 2-ary operators. In mathematics it's only because that abstract algebra is a generalization of the numbers and their common operators.
To study general n-aries in the same manner would require a lot of new experiences and heuristic superstructures.
However, Heap-theory do study ternary (3-ary) operations. And an other interesting example is planar ternary rings.
But obviously, humans like 2-aries more.
