Monoid, Definition and Examples :-

Definition: A non empty set G having binary operation “*” (say) is called Monoid if it satisfies the following axioms:

  • Closure Property w.r.t “*

i.e, a\ast b\in G\;\;\;\;\;\;\;\forall\;a,b\in G

  • Associative Law w.r.t “*

(a\ast b)\ast c=a\ast(b\ast c)\;\;\;\;\;\;:\;\forall\;a,b,c\in G

  • Identity element exist.

There is identity element e in G such that

a\ast e=e\ast a=a\;\;\;\;\;\;\;\;\forall\;a\in G

If the above three properties hold then the set is called Monoid.

We can also say semi group having identity element is called Monoid

Examples: Monoid

The following sets are Monoid

  • The set of Whole Numbers with respect to “Addition” and “Multiplication”.
  • The set of Natural Number with respect to “Multiplication”.
Spread the love
Azhar Ali

Azhar Ali

I graduated in Mathematics from the University of Sargodha, having master degree in Mathematics.

Leave a Reply

Your email address will not be published.

Mathematics is generally known as Math in US and Maths in the UK.

Contact Us

Copyright by Double Math. All Right Reserved 2019 to 2022