Example

(1) In the set $\mathbf{N}$ of natural numbers the stable subset under addition generated by {1} is the set of integers $\geq 1$; under multiplication the set {1} is stable.

(2) Given a law $\top$ on a set E, for a subset {h} consisting of a single element to be stable under the law $\top$ it is necessary and sufficient that $h \top h = h$; h is then said to be idempotent. For example, every element of a lattice is idempotent for each of the laws sup and inf.

(3) For an associative law $\top$ on a set E the stable subset generated by a set {a} consisting of a single element is the set of elements $\overline{\top}^n a$, where n runs through the set of integers $> 0$.