Definition:Identity (Abstract Algebra)/Left Identity

Definition

Let $\left({S, \circ}\right)$ be an algebraic structure.

An element $e_L \in S$ is called a left identity iff:

$\forall x \in S: e_L \circ x = x$

Also known as

• Left neutral element

Also see

• Right Identity
• Two-Sided Identity

Sources

• W.E. Deskins: Abstract Algebra (1964): Exercise $1.4: \ 9$
• J.A. Green: Sets and Groups (1965)... (previous)... (next): Exercise $4.4$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $4.3$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): Exercise $5.3$