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.