# Zero ring

In ring theory, a branch of mathematics, the **zero ring**^{[1]}^{[2]}^{[3]}^{[4]}^{[5]} or **trivial ring** is the unique ring (up to isomorphism) consisting of one element. (Less commonly, the term "zero ring" is used to refer to any rng of square zero, i.e., a rng in which *xy* = 0 for all *x* and *y*. This article refers to the one-element ring.)

In the category of rings, the zero ring is the terminal object, whereas the ring of integers **Z** is the initial object.