Definition:Ring Zero

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

The identity for ring addition is called the ring zero, or just the zero.

It is denoted $0_R$ (or just $0$ if there is no danger of ambiguity).

In Ring Product with Zero, it is shown that the ring zero is a zero element for the ring product, thereby justifying its name as the zero of the ring.