Question

An element a in a monoid is called an idempotent if ______________

(a) a^-1=a*a^-1

(b) a*a^2=a

(c) a^2=a*a=a

(d) a^3=a*a

I got this question during an online interview.

This intriguing question originated from Groups topic in division Groups of Discrete Mathematics

Answer 1

The correct option is (c) a^2=a*a=a

The best I can explain: An algebraic structure with a single associative binary operation and an Identity element are termed as a monoid. It is studied in semigroup theory. An element x in a monoid is called idempotent if a^2 = a*a = a.