Nullary operation

Summary

A nullary operation on a set $A$ is a finitary operation of arity $0$, that is, a map from the one-element set $A^0$ to $A$. Such a map is the same as the choice of one element of $A$, so nullary operations are the constants of an algebraic structure. Treating constants as operations lets identity elements, such as $0$ in a ring or $e$ in a group, be part of the signature.