The name of the magma would be "The natural numbers under addition".

The name of the magma would be "The integers under addition".

Once again consider the group of integers Z under addition.

This implies in particular that the class of Darboux functions is not closed under addition.

Here we have identity 1, as opposed to groups under addition where the identity is typically 0.

We conclude that is closed under addition and inverses, making it into a subgroup.

Lie rings are not Lie groups under addition, despite the name.

The rational numbers form a divisible group under addition.

Another familiar example might be the compact 2-torus or Euclidean space under addition.

The set of all quadratic integers is not closed even under addition.