An Abelian semigroup is a set whose elements are related by a binary operation (such as addition, rotation, etc.) that is closed, associative, and commutative.

A mathematical joke involving Abelian semigroups is given by Renteln and Dundes (2005).

Q: What's purple and commutes? A: An Abelian grape.

Q: What is lavender and commutes? A: An Abelian semigrape.