Definitions
1.NounAn element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.
2.Nouna left identity if
i
∗
x
=
x
{\displaystyle i*x=x}
for any
x
{\displaystyle x}
in the structure,
3.Nouna right identity,
x
∗
i
=
x
{\displaystyle x*i=x}
for any
x
{\displaystyle x}
in the structure,
4.Nounsimply an identity element or (for emphasis) a two-sided identity if both are true.