Definition:Ring Zero

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Definition

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

The identity for ring addition is called the ring zero (of $\left({R, +, \circ}\right)$).

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

When it is clear and unambiguous what is being discussed, the ring zero is often called just the zero.

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.