The identity elements are the lattice's top and its bottom, respectively.

Directly from the definition, one can show that the identity element e is unique.

The structure turns out be a loop with identity element 0.

The structure also turns out to be a loop with identity element 1.

Here 1 denotes the empty word, which represents the identity element.

Indeed, the center consists solely of the identity element and "x".

The empty set is an identity element for the operation of union.

Note that a group is in particular a pointed set, with the identity element as distinguished point.

Group means that addition associates and has an identity element, namely "0".

Simple groups have only two normal subgroups: the identity element, and M.