Integers form Subdomain of Rationals
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Theorem
The integral domain of integers $\left({\Z, +, \times}\right)$ forms a subdomain of the field of rational numbers.
Proof
The rational numbers are defined as the quotient field of the integers.
From its method of construction, it follows that the integers $\Z$ are a subset of the rational numbers $\Q$.
Hence the result, from the definition of subdomain.
$\blacksquare$
Sources
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.1$: Subrings: Examples $1$