Integers under Addition form Monoid

Theorem

The set of integers under addition $\struct {\Z, +}$ forms a monoid.


Proof

Follows directly from Integers under Addition form Abelian Group.

By definition, an abelian group is a group.

Also by definition, a group is a monoid.

Hence the result.

$\blacksquare$


Sources

  • 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.1$: Monoids
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