Ring of rational integers

Definition
The ring $$\mathbb{Z}$$, called the ring of rational integers or sometimes simply the ring of integers, is the ring whose elements are the rational integers, with the usual addition and multiplication. Explicitly, the underlying set is $$\{ \dots, -2, -1, 0, 1, 2, \dots \}$$ and the addition and multiplication are the usual ones.

The adjective rational is used in the name in circumstances where there may be potential confusion with the ring of integers in a number field.

This ring is the initial object in the category of commutative unital rings.