Definition:Identity (Abstract Algebra)/Right Identity

Definition

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

An element $e_R \in S$ is called a right identity iff:

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

Also known as

• Right neutral element

Also see

• Left 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 $4.5$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $4.3$
• Richard A. Dean: Elements of Abstract Algebra (1966): $\S 1.2$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): Exercise $5.3$