Algebra (universal algebra sense)

Definition
An algebra is defined as a set $$S$$ equipped with a collection of operators, each of which is a $$n$$-ary operation $$S^n \to S$$, where the value of $$n$$ could vary with the operator.

The "signature" of the algebra refers to the collection of arities of the operators.

We can study an algebra as a member of a suitable variety of algebras.