monoid in a sentence

Examples

1. In other words, a monoid is a semigroup with an identity element.
2. However, not every monoid sits inside a group.
3. A semigroup homomorphism between monoids preserves identity if it is a monoid homomorphism.
4. Particularly, if f is surjective, then it is a monoid homomorphism.
5. However this quotient itself is generally only a monoid.
6. Those axioms are formally similar to the monoid axioms.
7. A civil war erupts between the two Monoid factions.
8. An abstract mathematical foundation for synchronization primitives is given by the history monoid.
9. The collection of functions f _ i together with composition form a monoid.
10. Since the monoid is finite, for some.