Zero of Integral Domain is Unique

Theorem

Let $\struct {D, +, \times}$ be an integral domain.

Then the zero of $\struct {D, +, \times}$ is unique.

Proof

By definition, an integral domain is a ring.

The result the follows from Ring Zero is Unique.

$\blacksquare$

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 4$. Elementary Properties: Theorem $1 \ \text{(i)}$