Rational Numbers form Integral Domain
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Theorem
The set of rational numbers $\Q$ forms an integral domain under addition and multiplication: $\struct {\Q, +, \times}$.
Proof
Recall that Rational Numbers form Field.
The result then follows directly from Field is Integral Domain.
$\blacksquare$
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 3$. Definition of an Integral Domain