Integers form Commutative Ring with Unity

Theorem

The integers $\struct {\Z, +, \times}$ form a commutative ring with unity under addition and multiplication.


Proof

We have that:

$\struct {\Z, +, \times}$ form a commutative ring.
$\struct {\Z, +, \times}$ has a unity, and the unity is $1$.

$\blacksquare$


Sources

  • 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields: Example $1$
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