Is there a name for property $n+k=m+k\implies n=m$?

Question

Monoid of natural numbers with addition have such property, that for any $n,m, k \in \mathbb{N}$ if $n+k=m+k$ then $n=m$. Does this property have some name in English?

Answer 1

I usually see it being called the cancellation property. (because what you are doing above is cancelling the $k$s in both sides).

More precisely, as has been pointed out in the comment below, this is the right cancellation property.

Answer 2

This is the cancellation property. Bear in mind that it does not hold for a general monoid. The cancellative property is guaranteed by the existence of inverses, therefore, all monoids with inverses (groups) are cancellation structures.