Generated subalgebra

Summary

The subalgebra generated by a subset $X$ of an algebra is the smallest subalgebra that contains $X$. Its elements are the values of all terms in the operations applied to elements of $X$ and to the constants. The subgroup generated by a subset and the ideal generated by a subset are special cases of this idea. The map that sends $X$ to the subalgebra it generates is a closure operator, and an algebra generated by a finite set is finitely generated.