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

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

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

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

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

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

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

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

Within this identity elements of divine self-discovery continue to develop.

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

The identity element comes from a constant function which is non-zero.

When the operation is performed between them, the result is the identity element.

For multiplication and division, the identity element is 1.

It is the Identity element for addition and subtraction.

Each of the elements in the middle row when multiplied by itself gives -1 (where 1 is the identity element).

The identity element for this group is the translation with prescription "move zero miles in whatever direction you like".

The identity element for this group is zero.

Let be the differential at the identity element.

Identity element: One element of the group is special.

The associative operation and the identity element are defined pairwise.

In fact, as it turns out, is precisely the differential of at the identity element of the group.

A quasigroup with an identity element is called a loop.

The element is the multiplicative identity element of the ring.

With addition, the identity element is 0, because adding 0 to some number does not change the number.

Such identity elements have been used both in establishing theory and in computations; see below.