Editing Cancellation property (section)

== Examples of cancellative monoids and semigroups ==
The positive (equally non-negative) integers form a cancellative [[semigroup]] under addition. The non-negative integers form a cancellative [[monoid]] under addition.  Each of these is an example of a cancellative magma that is not a quasigroup.

Any free semigroup or monoid obeys the cancellative law, and in general, any semigroup or monoid that embeds into a group (as the above examples clearly do) will obey the cancellative law.

In a different vein, (a subsemigroup of) the multiplicative semigroup of elements of a [[Ring (mathematics)|ring]] that are not zero divisors (which is just the set of all nonzero elements if the ring in question is a [[Domain (ring theory)|domain]], like the integers) has the cancellation property. This remains valid even if the ring in question is noncommutative and/or nonunital.