The difference between Monoid and Semigroup

When used as nouns, monoid means a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation, whereas semigroup means any set for which there is a binary operation that is closed and associative.


Monoid is also adjective with the meaning: containing only one kind of metrical foot.

check bellow for the other definitions of Monoid and Semigroup

  1. Monoid as a noun (mathematics):

    A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

  1. Monoid as an adjective (prosody):

    Containing only one kind of metrical foot.

  1. Semigroup as a noun (mathematics):

    Any set for which there is a binary operation that is closed and associative.