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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*aI got this question during an online interview.This intriguing question originated from Groups topic in division Groups of Discrete Mathematics

Answer»

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.



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